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Jharkhand Board JAC Class 9 Maths Solutions Chapter 8 Quadrilaterals Ex 8.2 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions Chapter 8 Quadrilaterals Ex 8.2

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Question 1.
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig). AC is a diagonal. Show that:
(i) SR || AC and SR = \(\frac {1}{2}\)AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.

Answer:
(i) In ΔDAC,
R is the mid-point of DC and S is the mid-point of DA.
Thus by mid-point theorem, SR || AC and SR = \(\frac {1}{2}\)AC

(ii) In ΔBAC,
P is the mid-point of AB and Q is the mid-point of BC.
Thus by mid-point theorem, PQ || AC
and PQ = \(\frac {1}{2}\) AC
Also, SR = \(\frac {1}{2}\) AC
Thus, PQ = SR

(iii) SR || AC (Proved)
and, PQ || AC (Proved)
⇒ SR || PQ (Lines parallel to same line are parallel to each other)
Also, PQ = SR(Proved)
Thus, PQRS is a parallelogram.
(A quadrilateral in which a pair of sides is equal and parallel is a parallelogram).

Question 2.
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Answer:
Given: ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively.

To Prove: PQRS is a rectangle.

Construction: AC and BD are joined.

Proof: P and Q are mid-points of AB and BC respectively
⇒ PQ || AC and PQ = \(\frac{1}{2}\) AC …(i)
(By mid-point theorem)
Also, S are R are mid-points of AD and CD respectively, so, by mid-point theorem,
SR || AC and SR = \(\frac{1}{2}\)AC …(ii)
From (i) and (ii)
∴ PQ || SR and PQ = SR
⇒ PQRS is a parallelogram
As ABCD is a rhombus
AB = BC (sides of rhombus)
⇒ \(\frac{1}{2}\) AB = \(\frac{1}{2}\) BC
⇒ BP = BQ (As P and Q are mid-points of AB and BC respectively)
So, in ΔBPQ
∠BPQ = ∠BQP …(i)
(Angles opposite to equal sides are equal)
Also, BC = CD (Sides of rhombus)
⇒ \(\frac{1}{2}\) BC = \(\frac{1}{2}\) CD
⇒ CQ = CR (As Q and R are midpoint of BC and CD respectively)
So, in ACQR
∠CQR = ∠CRQ …(ii) (Angle opposites to equal sides are equal)
AB || CD (Opposite sides of a parallelogram)
⇒ ∠B + ∠C =180 …(iii)
(sum of angles on same sides of transversal is 180°)

In ΔBPQ, ∠BPQ + ∠BQP + ∠B = 180° (Angles sum property)
In ΔCQR, ∠CQR + ∠CRQ + ∠C = 180° (Angle sum property)

On adding both the equations, we get
∠BPQ + ∠BQP + ∠B + ∠CQR + ∠CRQ + ∠C = 360°
⇒ 180° + ∠BPQ + ∠BQP + ∠CQR + ∠CRQ = 360° [From (ii)]
⇒ 180° + 2 ∠BQP + 2 ∠CQR = 360° [From (i) and (ii)]
⇒ 2 (∠BQP + ∠CQR) = 360° – 180° = 180°
⇒ ∠BQP + ∠CQR = \(\frac{180°}{2}\) = 90° …(iv)

Now, ∠BQP + ∠CQR + ∠PQR = 180° (sum of angles on a straight line is 180°)
90° + ∠PQR = 180° [From (iv)]
⇒ ∠PQR = 180° – 90° = 90°
So, PQRS is a parallelogram in which one angle is 90°
⇒ PQRS is a rectangle.

Question 3.
ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Answer:
Given: ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively.
To Prove PQRS is a rhombus.
Construction: AC and BD are joined.
Proof: In ∆ABC
P and Q are the mid-points of AB and BC respectively
Thus, PQ || AC and PQ = \(\frac{1}{2}\) AC (Mid-point theorem) …(i)
In ∆ADC, SR AC and SR = \(\frac{1}{2}\) AC (Mid-point theorem) …(ii)
From (i) and (ii)
∴ PQ = SR and PQ || SR
⇒ PQRS is a parallelogram.
(As in quadrilateral PQRS one pair of opposite sides is equal and parallel to each other, so, it is a parallelogram.)
AB = CD (opposite sides of rectangle)
⇒ AB = CD
⇒ BP = CR(As P and R are midpoints of AB and CD respectively)

Consider ∆PBQ and ∆RCQ
BP = CR (Proved)
BQ = CQ [As Q is a mid-point of BC]
∠B = ∠C = 90° (As each angle of a rectangle ABCD is of 90°)
⇒ ΔPBQ ≅ ΔRCQ by SAS congruence criterion.
⇒ PQ = QR (CPCT)
Also, PQ = RS and PS = QR (As opposite sides of parallelogram are equal)
∴ PQ = QR = RS = PS
So, PQRS is a parallelogram in which all sides are equal.
⇒ PQRS is a rhombus.

Question 4.
ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig). Show that F is the mid-point of BC.

Answer:
Given: ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD.
To prove: F is the mid-point of BC.
Proof: BD intersects EF at G.
In ∆BAD,
E is the mid-point ofAD andalsoEG || AB.
Thus, G is the mid-point of BD (Converse of mid-point theorem)
Now, EG || AB
⇒ EF || AB
⇒ GF || AB
Also, AB || CD
∴ CD || GF (Lines parallel to same line are parallel to each other)

In ABCD, G is a mid-point of BD and CD || GF
⇒ F is a mid-point of BC (By converse of mid-point theorem)
Now, in ∆BDC,
G is the mid-point of BD and also GF || AB || DC.
Thus, F is the mid-point of BC (Converse of mid-point theorem)

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Question 5.
In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig). Show that the line segments AF and EC trisect the diagonal BD.

Answer:
Given: ABCD is a parallelogram. E and F are the mid-points of sides AB and CD respectively.
To prove: AF and EC trisect the diagonal BD.
Proof: ABCD is a parallelogram.
Therefore, AB || CD, also, AE || FC
Now, AB = CD (Opposite sides of parallelogram ABCD)
⇒ \(\frac{1}{2}\) AB = \(\frac{1}{2}\) CD
⇒ AE = FC (E and F are midpoints of sides AB and CD)
AECF is a parallelogram
(AE and CF are parallel and equal to each other)
AF || EC (Opposite sides of a parallelogram)

Now, in ADQC,
⇒ F is mid-point of side DC and FP || CQ (as AF || EC).
P is the mid-point of DQ (Converse of mid-point theorem)
⇒ DP = PQ …………(i)
Similarly, in AAPB,
E is mid point of side AB and EQ || AP (as AF || EC).
Q is the mid-point of PB (Converse of mid-point theorem)
⇒ PQ = QB ………….. (ii)

From equations (i) and (i),
DP = PQ = BQ
Hence, the line segments AF and EC trisect the diagonal BD.

Question 6.
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Answer:
Let ABCD be a quadrilateral and p, Q, R and S are the mid-points of AB, BC, CD and DA respectively.

Now, In ∆ACD, R and S are the mid-points of CD and DA respectively.
Thus SR || AC and SR = \(\frac{1}{2}\) AC (by mid-point theorem)
Also, in DABC, P and Q are mid-point of AB and BC respectively
⇒ PQ || AC and PQ = \(\frac{1}{2}\) AC (by mid-point theorem)
So, PQ = SR and PQ || SR.
Thus, PQRS is parallelogram, [since one pair of opposite sides is equal and parallel]
PR and QS are the diagonals of the parallelogram PQRS.
So, they will bisect each other. (As diagonals of a parallelogram bisect each other.)

Question 7.
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = \(\frac {1}{2}\)AB

Answer:
(i) In ∆ACB
M is the mid-point of AB and MD|| BC
Thus, D is the mid-point of AC (Converse of mid-point theorem)

(ii) ∠ACB = ∠ADM (Corresponding angles)
As ∠ACB = 90°
Thus, ∠ADM = 90° i.e. MD ⊥ AC

(iii) In ∆AMD and ∆CMD,
AD = CD (D is the mid-point of side AC)
∠ADM = ∠CDM (Each 90°)
DM = DM (common)
Thus, ΔADM ≅ ΔCDM by SAS congruence criterion.
AM = CM by CPCT
also, AM = \(\frac{1}{2}\) AB (M is mid point of AB)
Hence, CM = MA = \(\frac{1}{2}\) AB

JAC Board Class 9th Social Science Solutions Geography Chapter 2 Physical Features of India

JAC Class 9th Geography Physical Features of India InText Questions and Answers 

Find Out (Page No. 8)

Question 1.
The names of the glaciers and passes that lie in the Great Himalayas?
Answer:
Glaciers in the Great Himalayas: Siachin, Milam, Gangotri, Bhagirathi, Baltoro, Pindari.
Passes in the Great Himalayas: Burgil, Zoji La, Shipki La, Bara Lacha La, Nathu La, Bomdi La, Thaga La, Lipulekh La.

Question 2.
The name of the states where highest peaks are located.
Answer:

Highest Peaks	States
Kanchenjunga	Sikkim
Nanga Parbat	Jammu & Kashmir (Union Territory)
Nanda Devi	Uttarakhand
Kamet	Uttarakhand
Namcha Barwa	Arunachal Pradesh

Question 3.
Find the location of Mussoorie, Nainital, Ranikhet from your atlas and also name the state where they are located.
Answer:

Place	States
Mussoorie	Uttarakhand
Nainital	Uttarakhand
Ranikhet	Uttarakhand

JAC Class 9th Geography Physical Features of India Textbook Questions and Answers 

Question 1.
Choose the right answer from the four alternatives given below:
1. A landmass bounded by sea on three sides is referred to as:
(a) Coast
(b) Island
(c) Peninsula
(d) None of the above.
Answer:
(c) Peninsula

2. Mountain ranges in the eastern part of India forming its boundary with Myanmar are collectively called as:
(a) Himachal
(b) Uttarakhand
(c) Purvachal
(d) None of the above.
Answer:
(c) Purvachal

3. The Western Coastal Strip, south of Goa is referred to as:
(a) Coromandel
(b) Konkan
(c) Kannad
(d) Northern Circar
Answer:
(c) Kannad

4. The highest peak in the Eastern Ghats is:
(a) Anai Mudi
(b) Kanchenjunga
(c) Mahendragiri
(d) Khasi
Answer:
(c) Mahendragiri

Question 2.
Answer the following questions briefly:
1. What is the ‘bhabar’?
Answer:
Bhabar is a narrow belt of plain which is about 8 to 16 km wide. It is covered with pebbles deposited by rivers lying parallel to the slopes of the Shiwaliks.

2. Name the three major divisions of the Himalayas from North to South
Answer:
(a) The Great or Inner Himalayas or the ‘Himadri’.
(b) The Middle or Lesser Himalayas or the ‘Himachal’.
(c) The Outer Himalayas or the ‘Shiwaliks’.

3. Which plateau lies between the Aravalli and the Vindhya ranges?
Answer:
The Malwa Plateau.

4. Name the island group of India having a coral origin.
Answer:
The Lakshadweep Islands.

Question 3.
Distinguish between:
1. Bhangar and Khadar
2. Western Ghats and Eastern Ghats.
Answer:
1. Difference between Bhangar and Khadar:

Bhangar	Khadar
1. It is the older alluvial soil.	1. It is the newer alluvial soil.
2. It often contains kankar or nodules with calcium carbonates in sub-soil.	2. It is finer, more sandy and free from kankar nodules.
3. Bangar is not renewed frequently. Hence, it is less fertile.	3. Khadar is renewed frequently and is more fertile.
4. It is found away from the river at a higher ground level.	4. It is found near river channels, in deltas and in floodplains.

2. Difference between Western Ghats and Eastern Ghats:

Western Ghats	Eastern Ghats
1. The Western Ghats form the western side or edge of the Deccan Plateau.	1. The Eastern Ghats form the eastern side or edge of the Deccan Plateau.
2. These Ghats are regular and comparatively higher in elevation.	2. These ghats have a relatively lower elevation.
3. These lie parallel to the western coast.	3. These lie parallel to the eastern coast.
4. Their average elevation is 900-1600 metres.	4. Their average elevation is 600 metres.
5. They are continuous and can be crossed through passes only.	5. They are discontinuous and irregular and dissected by rivers draining into the Bay of Bengal.
6. The highest peak is Anai Mudi.	6. The highest peak is Mahendragiri.
7. Soil is highly fertile. Rice, spices, rubber, coconuts, cashew nuts, etc. are grown.	7. Soil is relatively less fertile. Groundnuts, rice, cotton, tobacco, coconuts, etc. are grown

Question 4.
Which are the major physiographic divisions of India? Contrast the relief of the Himalayan region with that of the Peninsular Plateau.
Answer:
The major physiographic divisions of India are:

1. The Himalayan Mountains
2. The Northern Plains
3. The Peninsular Plateau
4. The Indian Desert
5. The Coastal Plains
6. The Islands

The contrast between the relief of the Himalayan region with that of the Peninsular Plateau is as follows:

The Himalayan Region	The Peninsular Plateau
1. These are young fold mountains.	1. These are a part of the oldest structure of the earth’s crust.
2. These are formed of sedimentary rocks.	2. These are formed of igneous and metamorphic rocks.
3. These consists of three parallel ranges: Himadri, Himachal, Shiwa- liks.	3. It consists of two sections: The Central Highlands, The Deccan Plateau
4. Mostly glaciers and passes are found in this region.	4. Glaciers and passes are not found in this region.
5. These contain the highest mountains.	5. These are formed of low hills.
6. It is the origin of snow-fed, perennial rivers.	6. It has rainfed, seasonal rivers.

Question 5.
Give an account of the Northern Plains of India.
Answer:
A description of the Northern Plains of India is given hereunder:

1. The Northern plains lie to the south of the Himalayas.
2. The Northern plains have been formed by the interplay of the three major river systems, namely, the Indus, the Ganga and the Brahmaputra along with then tributaries.
3. It spreads over an area of 7 lakhs sq. km. It is about 2400 km long and 240 to 320 km broad.
4. It is formed of alluvial soil.
5. With a rich soil cover combined with adequate water supply and favourable climate, it is agriculturally a very productive part of India.
6. On the basis of the difference in the relief, the plain is divided into four sections
   • Bhabar,
   • Tarai,
   • Bhangar,
   •  Khadar.

Question 6.
Write short notes on the following:
1. The Indian Desert
2. The Central Highlands
3. The Island Groups of India.
Answer:
1. The Indian Desert:
(a) The Indian desert lies towards the western margins of the Aravalli Hills.

(b) It is an undulating sandy plain covered with sand dunes called Barchans.

(c) This region receives very low rainfall: below 150 mm per year.

(d) It has an arid climate with low vegetation cover.

(e) Luni is the only large river in this region.

2. The Central Highlands :
(a) The part of the Peninsular plateau lying to the North of the Narmada river, covering a major area of the Malwa plateau, is known as the Central Highlands.

(b) The Vindhyan range is bounded by the Satpura range on the south and the Aravallis on the North-West. The further westward extension gradually merges with the sandy and rocky desert of Rajasthan.

(c) The flow of the rivers draining this region, namely, the Chambal, the Kalisindh, the Betwa and the Ken is from South-West to North-East, thus, indicating the slope.

(d) The Central Highlands are wider in the west but narrower in the east. The eastward extensions of this plateau are locally known as the Bundelkhand and Baghelkhand.

(e) The Chotanagpur plateau marks the further eastward extension, drained by the Damodar river.

3. The Island Groups of India:
(a) The Lakshadweep and the Andaman and Nicobar islands are the two main island groups of India.

(b) The Lakshadweep Islands group lies close to the Malabar coast of Kerala. This group of islands is composed of small coral islands. It covers a small area of 32 sq.km. Kavaratti island is the capital of Lakshadweep.

(c) The Andaman and Nicobar islands located in the Bay of Bengal extend from North to South. They are bigger in size and are more numerous and scattered. Port Blair is the capital of this island group.

On an outline map of India, show the following:
1. Mountain and hill ranges: the Karakoram, the Zaskar, The Patkai Bum, the Jaintia, le Vindhya range, the Aravalli, and the Cardamom hills.
2. Peaks: K2, Kanchenjunga, Nanga Parbat and the Anai Mudi.
3. Plateaus: Chhota Nagpur and Malwa.
4. The Indian Desert, Western Ghats, Lakshadweep Islands.
Answer:

Locate the peaks, passes, ranges, plateaus, hills and dunes hidden in the puzzle. Try t find where these features are located. You may start your search horizontally, vertically diagonally.

Answer:
Peaks: Kanchenjunga, Everest, Anai Mudi, Aravali

Passes: Nathu La, Shipki La, Bomdi La.

Ranges: Maikal, Sahyadri, Vindhyan.

Plateau: Chotanagpur, Malwa.

Hills: Jaintia, Kaimur, Garo, Nilgiri, Cardamom

Students can locate the above features on a map under the guidance of their teacher

JAC Class 9 Social Science Solutions

JAC Board Class 9th Social Science Solutions History Chapter 4 Forest Society and Colonialism

JAC Class 9th History Forest Society and Colonialism InText Questions and Answers 

Activity (Page No. 81)

Question 1.
Each mile of railway track required between 1,760 and 2,000 sleepers. If one average sized tree yields 3 to 5 sleepers for a 3 metre wide broad gauge track, calculate approximately how many trees would have to be cut to lay one mile of track.
Answer:
Average number of sleepers required to lay one mile railway track = \(\frac{1760+2000}{2}=1880 \)
Average number of sleepers made by 1 tree = \(\frac{3+5}{2}=4\)
Thus, number of trees would have to be cut to lay one mile of track = \(\frac{1880}{4}=470 \)
Approximately, 470 trees would have to be cut to lay one mile of track.

Activity (Page No. 83)

Question 1.
If you were the Government of India in 1862 and responsible for supplying the railways with sleepers and fuel on such a large scale, what were the steps you would have taken?
Answer:
if I were the Government of India in 1862 and responsible for supplying the railways with sleepers and fuel on such a large scale, I would have taken the following steps:

1. I would have planned a systematic utilisation of the forest wealth; rules about the use of forest resources would have been framed.
2. Instead of using wood, iron or stone would have been used for making sleepers. Coal is used as fuel for running the railways engines.
3. Along with cutting down the forests, a plan for afforestation on a large-scale would have been initiated simultaneously.

Activity (Page No. 86)

Question 1.
Children living around forest areas can often identify hundreds of species of trees and plants. How many species of trees can you name?
Answer:
Fruiting Trees: Mango, Guava, Lemon, Banana etc.
Medicinal Plants: Tulsi, Neem, Babool, Sarpagandha etc.

Activity (Page No. 96)

Question 1.
Have there been changes in forest areas where you live ? Find out what these changes are and why they have happened.
Answer:
Yes, there have been many changes in forest areas where I live. These changes are as follows :

1. There have been strict restrictions on the hunting of wild animals.
2. A tremendous increase in the number of wild animals could be seen in these areas.
3. There have been many check posts of forests protection offices established.
4. Smuggling of elephant’s teeth and skin of tiger has been strictly prohibited.
5. There have been cleaning of rivers flowing through the forest areas. These changes have been made to protect the environment.

Question 2.
Write a dialogue between a colonial forester and an adivasi discussing the issue of hunting in the forest.
Answer:
A Sample dialouge is given below:
Colonial Forester: Who are you? What are you doing in this forest?

Adivasi: Sir, I am an adivasi. I live in nearby village. I came here to collect fruits and for hunting rabbits.

Colonial Forester: Don’t you know about the prohibition of hunting in forests?

Adivasi: But Sir, my children are hungry since five days. I came here to fulfill their food requirements.

Colonial Forester: I don’t care about it. I just know that hunting in forest is illegal. It is a crime and you will deserve a punishment for this.

Adivasi: But sir, this is our forest. Means if we, advasis, are restricted from hunting, then what other work we people will do? How will we care our family and our daily needs? Our family will die of starvation.

Colonial Forester: Look, you are arguing with me

Adivasi: Sir, we are dependent on these forests. Please let us do hunting. We will give you a share of our hunt.

Colonial Forester: Shut up! No, not at all. I have to report about you to our Forest Officer. Come with me.
Colonial forester arrests the adivasi and takes him away to his officer.

JAC Class 9th History Forest Society and Colonialism Textbook Questions and Answers 

Question 1.
Discuss how the changes in forest management in the colonial period affected the*) following groups of people:
1. Shifting cultivators
2. Nomadic and pastoralist communities
3. Firms trading in timber/forest produce.
4. Plantation owners
5. Kings/British officials engaged in shikar (hunting).
Answer:
1. Shifting cultivators:
Restriction on shifting cultivation resulted in displacement of many communities from their homes in the forests. Many were reduced to the level of starvation. Many changed their occupation and some became labourers.

2. Nomadic and Pastoralist Communities:
The forest laws deprived people of their customary rights and that meant severe hardship for the Nomadic and Pastoralist communities. They could not cut wood for their houses could not graze their cattle or collect fruits and roots, and hunting and fishing were declared illegal. Some of the nomadic communities began to be called ‘Criminal Tribes’ and were instead forced to work in factories, mines and plantations under government supervision. They were also recruited for work in plantations. Their wages were low and conditions of work were very bad.

3. Firms trading in timber/forest produce:
Under the new forest laws, lucrative opportunities opened up in the trade of forest products, specially timber. However, the trade was completely regulated under colonial government. The British governments gave many large European trading firms the sole right to trade in the forest products of particular areas.

4. Plantation owners:
Changes in forest management favoured the plantation owners who were mostly Europeans. They were given free land to destroy natural forests to make way for tea, coffee and rubber plantation, to meet the Europeans’ growing need for these commodities. But the workers on these plantations were paid very low wages. They had to live in very bad conditions;

5. Kings/British officials engaged in shikar (hunting):
Hunting of tiger and other animals had been a part of the culture of the court and nobility for centuries. The British saw large animals as a sign of a wild, primitive and savage society. Therefore, they provided strong incentives to encourage people to take guns and kill these dangerous animals. This hunting as a game for pleasure flourished under the new forest laws.

Question 2.
What are the similarities between colonial management of the forests in Bastar and in Java ?
Answer:
Bastar is located in the southernmost part of Chhattisgarh in India, while Java is located in Indonesia. The colonial power in India was the British, while in Java it was the Dutch. The similarities between colonial management of the forests in Bastar and Java are as follows :

1. A large number of trees were cut down for shipbuilding and railways.
2. There was restriction on hunting at the both places.
3. Nomads and pastoralists were restricted to enter the forests.
4. In both of the places defaulters of forests laws were punished, harassed and
5. Both Bastar and Java witnessed rebellion against rulers.
6. Both the governments displaced the local communities from their traditional livelihood in order to make full use of the forest produce.
7. Both restricted the villagers from practising shifting cultivation.

Question 3.
Between 1880 and 1920, forest cover in the Indian subcontinent declined by 9.7 million hectares, from 108.6 million hectares to 98.9 million hectares. Discuss the role of the following factors in this decline :
1. Railways
2. Shipbuilding
3. Agricultural expansion .
4. Commercial farming
5. Tea/Coffee plantations
6. Adivasis and other peasant users.

1. Railways:
Colonial rulers needed sleepers to lay railway lines which were made of hard wood. Each mile of railway track required more than 1800 sleepers. By 1890, about 25,500 km of track had been laid. As the railway tracks spread through India, a larger and larger number of trees were felled. Forests around the railway tracks started disappearing fast. Wood was used as a fuel to run the locomotives.

2. Shipbuilding:
By the early nineteenth century, there was shortage of oak
trees in England which were the basic input for ship industry. This created a problem of timber supply for the Royal Navy. By the 1820s, search parties were sent to explore the forest resources of India. Within a decade, trees were being felled on a massive scale and vast quantities of timber were being exported from India. ‘

3. Agricultural expansion: In 1600, approximately one sixth of the total of India’s land area was under cultivation but now it is 42% because of the increasing population. In the early nineteenth century, the colonial state thought that forests were unproductive. They were considered to be wilderness that had to be brought under cultivation, so that the land could yield agricultural products and revenue, and enhance the income of the state. So, between 1880 and 1920, cultivated area rose by 6.7 million hectares.

4. Commercial farming:
Commercial farming was also responsible for deforestation. The Britishers directly encouraged the production of commercial crops like jute, sugar, cotton, tea, wheat etc. They encouraged their production because these crops were required as raw material and cereals were required to feed the growing urban population of Europe. Thus, forests were cleared for growing commercial crops.

5. Tea/Coffee plantations:
Large areas of forests were also cleared to make way for plantation crops like tea, coffee and rubber. These crops were grown to meet the Europeans’ growing demand. Plantation owners made big profits, making the workers work for long hours and at low wages.

6. Adivasis and other peasant users:
Adivasis and peasants cleared forests for shifting cultivation and commercial farming. Apart from this, they cut down the trees for fuel.

Question 4.
Why are forests affected by wars?
Answer:
Forests are affected by wars due to various reasons which are as follow :

1. In the modern times, the defending armies hid themselves and their war material under the cover of the thick forests to avoid detection. As such the enemy forces target forest areas to capture the opposing soldiers and their war materials.
2. Because of pre-occupation of the participant countries in the war, many proposals for promoting the forests culture have to be abandoned half-way and many such forests became prey of neglect.
3. To meet war needs, sometimes forests are cut indiscriminately and as a result forests vanished with no times one after the other.
4. Fearing the capture of forest areas by the enemy, sometimes the existing governments themselves cut down the trees recklessly, destroy the saw mills and bum huge piles of logs.
5. Finding the forest staff in difficulty and engaged during the war times, some people expand their agricultural land at the cost of the forest land.

JAC Class 9 Social Science Solutions

JAC Board Class 9th Social Science Solutions History Chapter 3 Nazism and the Rise of Hitler

JAC Class 9th History Nazism and the Rise of Hitler InText Questions and Answers 

Activity (Page No. 61)

Question 1.
Read Sources A and B :
1. What do they tell you about Hitler’s imperial ambition?
2. What do you think Mahatma Gandhi would have said to Hitler about these ideas?
Answer:
1. The two texts (Source ‘A’ and Source ‘B’) tell that Hitler’s imperialistic ambition was to expand the boundaries of Germany till wherever they could possibly reach. In Source ‘A’ he believed that an aggressive nation will find methods to adjust its teritory to its population’s size. In source ‘B’, he was comparing Germany’s size to that of Russia and wanted Germany to become a world power of similar size.

2. Mahatma Gandhi held a strongly opposite view. He believed in non-violence and peaceful co-existence of different races, communities and nations. Gandhi would have told Hitler to drop the idea of aggression against other nations from his mind, as violence begets violence.

Activity (Page No. 63)

Question 1.
What does citizenship mean to you? Look at Chapters 1 and 3 and write 200 words on how the French Revolution and Nazism defined citizenship.
Answer:
For me, Citizenship is a fundamental right of any person to live in his birth country or any favourable country. The French Revolution and Nazism both defined citizenship with different points of view.

1. French Revolution:
As per the French Revolution, all men are equal and free by birth and their rights are also equal. Freedom, prosperity, protection and protest against exploitation are the initial rights of a citizen. All men are free to express their views and to reside at any place of their choice. In a democratic country, there is rule of law and no one is above the law.

2. Citizenship in the view of Nazism:
Nazism defined citizenship on the basis of racial hierarchy. Therefore, they denied the citizenship of the Jews. Moreover, they treated them very cruelly and threw out them from Germany.

Question 2.
What did the Nuremberg Laws mean to the ‘undesirables’ in Nazi Germany? What other legal measures were taken against them to make them feel unwanted?
Answer:
Basically, The Nuremberg Laws of citizenship of September 1935, meant that the ‘undesirables’ had no right to live along with the other citizens. These included Jews, Gypsies, Blacks and other nationalities like Polish and Russian people. Following other legal measures were taken against them to make them feel unwanted :

1. Only persons of German or related blood would henceforth to be German citizens, enjoying the protection of the German empire.
2. Marriages between Jews and Germans were forbidden.
3. Extramarital relations between Jews and Germans were declared a crime.

Activity (Page No. 66)

Question 1.
If you were a student sitting in one of these classes, how would you have felt towards Jews?
Answer:
If I had been a student sitting in one of these classes, I would have felt very bad as I would be missing my friends who used to play with me earlier. I would have felt sympathetic towards them and would have hated the Nazi government for this action. Other legal measures included:

1. Boycott of Jewish businesses.
2. Expulsion from government services.
3. Forced selling and confiscation of their properties.
4. Jews were forbidden to hoist the national flag.

Question 2.
Have you ever thought of the stereotyped of other communities that people around you believe in? How have they acquired them?
Answer:
I have thought about the stereotypes of other communities that we believe in. They usually inherit from their forefathers and the traditions and customs of the community to which they belong.

Activity (Page No. 67)

Question 1.
Look at Figs. 23, 24 and 27. Imagine yourself to be a Jew or a Pole in Nazi Germany. It is September 1941, and the law forcing Jews to wear the Star of David has just been declared. Write an account of one day in your life.
Answer:
I was roaming on the streets of Berlin. I was very hungry and thirsty. I was searching for a gentle German lady who could give me a loaf of bread. But Alas! This could be my never ending search. Soon I heard a noise of a crowd which was chasing some boys. The people told me to enter in that crowd. All people wore a Star of David. As I felt that they were also Jews like me, I also ran along with them but unfortunately I was caught with them and all of us were thrown into the concentration camp.

Activity (Page No. 69)

Question 1.
How would you have reacted to Hitler’s ideas if you were:
1. A Jewish woman
2. A non-Jewish German woman
Answer:

1. As a Jewish woman, I would have reacted with fear sense of insecurity, anger and hatred.
2. As a non-Jewish German woman, I would try to mobilise support secretly and help the victims of Nazi persecution.

Question 2.
What do you think this poster (Fig. 28) is trying to depict?
Answer:
I think this poster is trying to make mockery of the Jews by projecting them as money hungry.

Activity (Page No. 70)

Question 1.
Look at Figs. 29 and 30 and answer the following: What do they tell us about Nazi propaganda? How are the Nazis trying to mobilise different sections of the population?
Answer:
From figure 29 and 30, we learn about the Nazi propaganda that they conduct in order to win the support of the working classes. The second poster is telling them to vote for Hitler, who has fought of the frontline in World War II. The first poster is condemning the Capitalists and Bolsheviks, because they are enemies of Nazism. By this method, the Nazis tried to mobilise different sections of the society to their cause.

Activity (Page No. 71)

Question 1.
Why does Erna Kranz say, ‘I could only say for myself? How do you view her opinion?
Answer:
Erna Kranz was telling Lawrence Rees about his personal experiences of the 1930s. According to him, people were now seeing hope. People’s salary has increased. Germany will develop again afresh. Now a good era is about to begin.

Activity (Page No. 74)

Question 1.
Write a one page history of Germany.
1. As a school child in Nazi Germany.
2. As a Jewish survivor of a concentration camp.
3. As a political opponent of the Nazi regime.
Answer:
1. As a school child in Nazi Germany:
In Nazi Germany, the condition of school children was very miserable. The Nazis started their ideological training when the child was three years old. As soon as he even started to think, he was given a small flag to wave. Ten-year-olds had to enter Jungvolk, a Nazi school. At 14, all boys had to join the Nazi youth organization, Hitler Youth, where they learnt to worship war, glorify aggression and violence, condemn democracy, and hate Jewish communities, gypsies and all those categorised as ‘undesirable’.

After a period of rigorous ideological and physical training, they joined the labour service, usually at the age of 18. Then they had to serve in the armed forces and enter one of the Nazi organisations. In this way, their whole life was spent under the conservative thinking which was forced on them. School children were segregated from their Jewish friends. They had to read textbooks that were prepared only for advertising the Nazi ideas. Even the function of sports was to nurture a spirit of violence and aggression among children. They were forced to choose boxing for sport.

2. As a Jewish survivor of a concentration camp:
The German Nazis will be always remembered for their brutality towards the Jews. This is a black chapter of German history. Jews from Jewish houses, concentration camps and ghettos from different parts of Europe were brought to death factories by goods trains where they were brutally tortured. I am afraid still now to remember those incidents.

Although I was alive there, but I felt my death hundred times. Jews were often persecuted through periodic organised violence and torture and then sent to concentration camps. Finally, they were left in gas chambers for death. The life of Jews were very miserable even out of the concentration camps. They were terrorised, pauperised and segregated from the society, and forced to leave the country.

All Jews had to wear a yellow Star of David on their breasts. This identity mark was stamped on their passport and houses too. They were kept in Jewish houses like ghettos that became sites of extreme misery and poverty. In any case of suspection or violation of law, they were sent to concentration camps where a new period of torture was started which resulted into their death. Millions of Jews were killed in gas chambers in front of our eyes.

3. As a political opponent of the Nazi regime:
Nazi rule in Germany was built up on the foot of propaganda. Nothing would be found to acquire new territories by war. This never brings a long peace and prosperity in any country. Although, I am a strong supporter of nationalism, but Nazi meaning for nationalism was totally disagreeable to me.

To achieve German nationalism, an investment of large amount on army is not right from any point of view. Nazi behaviour towards women and children was totally unfair. To hate the Jews and worship Hitler was complete injustice to them. The history will never forgive the Nazis for their failed trial to mislead the German masses by the propaganda of their uncivilian characters.

Question 2.
Imagine that you are Helmuth. You have had many Jewish friends in school and do not believe that Jews are bad. Write a paragraph on what you would say to your father.
Answer:
Dear Papa, I have many Jewish friends. We are learning to hate the Jews in our school. Jews have been thrown out from the school and taken to gas chambers for death. After all, what sin have they committed for which they are being treated like this? Why they are doing this to the Jews? Why Jews are sentenced to death illegally?

Are they not human beings like us? Do they not feel like us? Can you imagine if someone brought me to gas chamber and leave me there for death? Is the acceptance of Jewish religion a crime? If yes, then what will be the punishment for Christians whatever they are doing with Jews? Jesus will never forgive the Nazis for their brutality towards The Jews.

JAC Class 9th History Nazism and the Rise of Hitler Textbook Questions and Answers 

Question 1.
Describe the problems faced by the Weimar Republic.
Answer:
Weimar Republic faced many problems right since its birth. These were as follows:

1. This Republic carried the burden of war guilt and was financially disabled by being forced to pay war compensation.
2. Hyperinflation made the German mark valueless and caused immense hardship for the common man.This economic crisis led to widespread inflation, misery and despair.
3. In the Weimar Republic, both the communists and socialists became staunch enemies and could not make common cause against Adolf Hitler.
4. Both revolutionaries and militant nationalists craved for radical solutions, which was not easy. Within its short life, the Weimar Republic saw twenty different cabinets and the liberal use of Article 48. All this created a political crisis in Germany.
5. It became very unpopular among the Germans because it lost the vanity of the nation to the hands of Allied powers.

Question 2.
Discuss why Nazism became popular in Germany by 1930.
Answer:
The principal causes responsible for popularising Nazism in Germany can be summed up as follows :
1. Discontent due to the Treaty of Versailles:
After defeating the Germany, Allies had imposed many unjust conditions on Germany. It was forced to accept them under the threat of aggression. The aggression gave rise to Nazism in Germany.

2. Political Instability in Germany:
Under the Weimar Republic, there existed political instability. Between 1919-1933 A.D. as many as 21 coalition governments were formed and dissolved. Policies changed frequently. Democracy failed to give any relief to the people. Hitler promised a stable and strong government. He won the support of the people.

3. Unfaithful democracy in Germany:
Germany had no tradition of running a parliamentary democracy. Germany to say the least was “a democracy without democrat”. The democracy was against the German culture and tradition. Therefore, people could not understand the functional activities of parliamentary institutions. There were deep political differences between the communists and the Nazis. Because of above reasons democracy failed to achieve faith among German citizens.

4. The Economic Crisis:
Unemployment, inflation, price-rise, ruin of German trade and industry, coupled with general world depression created economic disaster of the worst order in Germany. Hitler blamed the Weimar republic for the plight of the masses and promised relief to the people on economic front, and he won their confidence.

5. Threat of Communism:
The communists in Germany tried to stage a revolution on the pattern of the Soviet revolution of 1917 A.D. Thus, the German capitalists extended full support to Hitler’s Nazi Party as the party was against socialism.

6. Hitler’s Dynamic Personality:
Hitler had a dynamic personality. He was influential and charming. He was a great organiser, an excellent orator and a tireless worker. His passion and his words moved people. He promised to build a strong nation, undo the injustice of the Versailles Treaty and restore the dignity of the German people. His appeal touched the emotions of the people.

Question 3.
What are the peculiar features of Nazi thinking?
Answer:
The peculiar features of Nazi thinking were as follows:

1. They believed that the strong should rule the world and the rest should accept their leadership.
2. They believed in racial hierarchy, where the Nordic German1 Aryans were at the top and the Jews at the lowest rung.
3. The Nazis believed that the Jews were their irreconcilable enemies. So the Jews were victimized and killed.
4. The Nazis believed in the geopolitical concept of ‘Lebensraum’ or living space i.e., new territories had to be acquired for the German nation.
5. Women were seen as mere bearers of the Aryan culture and race.

Question 4.
Explain why Nazi propaganda was effective in creating a hatred for Jews.
Answer:
Nazi propaganda was effective in creating a hatred for Jews because of the following reasons :
1. Role of Traditional Christians:
Jews remained the worst sufferers in Nazi Germany. Nazi’s hatred for Jews had a precursor in the traditional Christian hostility towards Jews. They had been stereotyped as killers of Christ and usurers. Until medieval times, Jews were barred from owning land. They survived mainly through trade and money lending.

2. Various Theories:
The Nazis started using theories of Darwin” and Herbert Spencer to propagate against Jews. So, people started justifying their hatred for Jews as they were considered inferior race and had no right to survive according to these two theories.

3. Propaganda at School Level:
Nazis started their propaganda right from school level. School textbooks were rewritten to justify ideas of race.

4. Propaganda at Home:
Motherhood was also used by Nazis to propagate against the Jews. Mothers were supposed to teach their children Nazi values. There was a code of conduct for all the women.

5. Propaganda through Press and Radio:
The Nazi regime needed languages and media with care to propagate against the Jews. Nazi ideas were spread through visual images like films, radio, movies etc. Jews were shown as rats and pests. Various code words were used to eliminate the Jews to protect the government from the world’s reaction.

Question 5.
Explain what role women had in Nazi society. Return to Chapter 1 on the French revolution. Write a paragraph comparing and contrasting the role of women in the two periods.
Answer:
Role of Women in Nazi Society : Equality of opportunity for both sexes had become an accepted principle by democracy everywhere in the world, but in Nazi Germany, a woman was valuable only as “a mother of pure Nordic (Aryan) children”. She was encouraged to preserve the purity of Aryan race and never to get involved in love affair with a Jew or a Russian or a Pole.

Those held guilty of love making with such persons were paraded with “shaven heads” through the streets. On the other hand, women would take pride in giving birth to as many children as they could. A comparative study of the Role of Women during Nazi Rule and the French Revolution:

1. Women played an important role in the French Revolution. They took equal part in social and political developments of their country. On the other hand, the Nazis thought that it was wrong on the part of women to demand their rights.
2. Most of the French women had to work for a living along with the men, but German women were not allowed to work along with men.
3. In France, both men and women were treated equal, but in Germany, women were considered nothing more than the bearers of the Aryan culture and race.
4. French women were free to change their patterns, but there was a code of conduct for the German women. They were not allowed to mix with anyone except Nordic Aryans.

Question 6.
In what ways did the Nazi state seek to establish total control over its people?
Answer:
The Nazi state seek to establish total control over its people in the following ways:
1. Political control:
Politically Germany was a single-party system where only the Nazi party could wield power. All the other parties had been banned. The state was led by as all powerful leaders. Even the army and the judiciary were controlled by the Nazi party.

2. Economic Control:
The Minister of Economies controlled all financial institutions such as banks and insurance companies. He also exercised rigid control over industries, factories and trading and commercial activities. In order to supply food to soldiers, many articles of food were rationed. Wage rates and prices of all articles of daily use were fixed.

3. Control over Education:
To propagate Nazism, the whole education system was put under the control of the state. School textbooks were rewritten. Racial science was introduced to justify the idea of race. Jewish teachers and Jewish children were thrown out of the school.

4. Control over social and cultural life:
The whole of the media, educational system and sports activities were controlled by the state. Women were declared second class citizens in Germany. Their concern should be their kitchens and giving birth to healthy children. Hundreds of thousands of Germans suffering from hereditary diseases were sterilized and thus prevented from giving birth to weak and unhealthy children.

JAC Class 9 Social Science Solutions

Jharkhand Board JAC Class 9 Maths Solutions Chapter 7 Triangles Ex 7.4 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions Chapter 7 Triangles Ex 7.4

Page-132

Question 1.
Show that in a right angled triangle, the hypotenuse is the longest side

Answer:
ABC is a triangle right angled at B.
Now,
∠A + ∠B + ∠C = 180°
⇒ ∠A + ∠C = 90° (∵ ∠B = 90°)
So ∠A < 90° and ∠C < 90°
⇒ ∠B > ∠A and ∠B > ∠C
⇒ AC > BC and AC > AB [As side opposite to larger angle is longer]

Question 2.
In Fig, sides AB and AC of AABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.

Answer:
Given: ∠PBC < ∠QCB
Proof: ∠ABC + ∠PBC = 180°
⇒ ∠PBC = 180° – ∠ABC …(i)
Also, ∠ACB + ∠QCB = 180°
⇒ ∠QCB = 180° -∠ACB
⇒ ∠PBC < ∠QCB (Given)
⇒ 180° – ∠ABC < 180° – ∠ACB
(From (i) and (ii))
⇒ – ∠ABC < – ∠ACB
⇒ ∠ABC > ∠ACB
⇒ AC > AB (As sides opposite to larger angle is longer.)

Question 3.
In Fig, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

Answer:
Given: ∠B < ∠A and ∠C < ∠D
Proof: In ΔAOB,
∠B < ∠A ⇒ AO < BO ……….(i)
(Side opposite to smaller angle is smaller)
In ΔCOD
∠C < ∠D ⇒ DO < CO…(ii)
(Side opposite to smaller angle is smaller)
Adding (i) and (ii)
AO + OD < BO + OC
⇒ AD < BC

Question 4.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig). Show that ∠A > ∠C and ∠B > ∠D.

Answer:
In ΔABD,
AB < AD (As AB is the shortest side)
∴ ∠ADB < ∠ABD ……..(i) (Angle opposite to longer side is larger.)
Now, in ΔBCD,
BC < DC (As CD is the longest side)
∴ ∠BDC < ∠CBD …..(ii) (Angle opposite to longer side is larger.)
Adding (i) and (ii), we get
∠ADB + ∠BDC < ∠ABD + ∠CBD
⇒ ∠ADC < ∠ABC
⇒ ∠B > ∠D
Similarly, in Δ ABC,
AB < BC (As AB is the smallest side)
∠ACB < ∠B AC …(iii) (Angle opposite to longer side is larger)
Now, in ΔADC,
AD < DC (As CD is the longest side)
∠DCA < ∠DAC …(iv) (Angle opposite to longer side is larger)
Adding (iii) and (iv), we get
∠ACB + ∠DCA < ∠BAC + ∠DAC
⇒ ∠BCD < ∠BAD
⇒ ∠A > ∠C

Question 5.
In Fig, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ

Answer:
Given: PR > PQ and PS bisects ∠QPR
To prove: ∠PSR > ∠PSQ
Proof: ∠PQR > ∠PRQ …….(i)
(PR > PQ as angle opposite to longer side is larger)
∠QPS = ∠RPS …(ii) (PSbisects ∠QPR)
∠PSR = ∠PQR + ∠QPS ………(iii)
(exterior angle of a triangle equals the sum of opposite interior angles)
∠PSQ = ∠PRQ + ∠RPS …(iv)
(exterior angle of a triangle equals the sum of opposite interior angles)
Adding (i) and (ii)
∠PQR + ∠QPS > ∠PRQ + ∠RPS
⇒ ∠PSR > ∠PSQ [from (iii) and (iv)]

Page-133

Question 6.
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Answer:
Given: Let l is a line segment and B is a point lying on it. We draw a line segment AB perpendicular to 1. Let C be any other point on 1.
To prove: AB < AC
Proof: In ∆ABC,
∠B = 90°
Now, ∠A + ∠B + ∠C = 180°
⇒ ∠A + ∠C = 90°
⇒ ∠C < 90° (∠B = 90°)
⇒ ∠C < ∠B
∴ ∠C must be acute angle or ∠C < ∠B
⇒ AB < AC (Side opposite to the larger angle is longer.)

Jharkhand Board JAC Class 10 Sanskrit Solutions रचना वाक्य निर्माणम् Questions and Answers, Notes Pdf.

JAC Board Class 10th Sanskrit Rachana वाक्य निर्माणम्

पद एवं उनके वाक्य प्रयोग :

पदाधारितवाक्यानां निर्माणम्

1. राजानं – सभासदः राजानं पश्यन्ति।
2. मन्त्रिणा राजा मन्त्रिणा सह वार्ता करोति।
3. विदुषे – राजा विदुषे ग्रन्थं ददाति।
4. राज्ञः – राज्ञः वचनं पालनीयम्।

सर्वनामशब्दाधारितवाक्यानाम् निर्माणम्

1. एषा – एषा मम भगिनी।
2. भवती – भवती अध्यापिका अस्ति।
3. यूयं – यूयं संस्कृतं पठत।
4. सः – सः बालकः अस्ति।

उपसर्गाधारितवाक्यानाम् निर्माणम्

1. अधिवसति – शिवः कैलासम् अधिवसति।
2. अपकरोति – दुर्जनः सदा अपकरोति।
3. प्रभवति – हिमालयात् गङ्गा प्रभवति।
4. संहरति – राजा शत्रून् संहरति।

अव्ययाधारितवाक्यानाम् निर्माणम्

1. सदा – बटुः सदा पठति।
2. समया – ग्रामं समया नदी वहति।
3. प्रभृतिः – अहं बाल्यकालात् प्रभृतिः अत्र वसामि।
4. इदानीं – इदानी वृष्टिः भवति।

हलन्तशब्दाधारितवाक्यानाम् निर्माणम्

1. श्रद्धावान् – श्रद्धावान् ज्ञानं लभते।
2. वाक् – वाक् मधुरा अस्ति।
3. सरित् – सरितः वहन्ति।
4. महत् – रोगिसेवा महत् कार्यं भवति।

अजन्तशब्दाधारितवाक्यानाम् निर्माणम्

1. विष्णुः – विश्वस्य पालकः विष्णुः।
2. लता – अने शोभते लता।
3. धेनुः – नन्दिनी वसिष्ठस्य धेनुः।
4. अश्रुः – बालकस्य नेत्राभ्याम् एकैकम् अश्रुः पतति।

कारकाधारितवाक्यानाम् निर्माणम्

1. धिक् – धिक् दुर्जनम्। (दृष्टि व्यक्ति को धिक्कार है।)
2. सह – पुत्रः पित्रा सह गच्छति। (पुत्र पिता के साथ जाता है।)
रमेशः मया सह पठति। (रमेश मेरे साथ पढ़ता है।)
बालकाः मित्रः सह क्रीडन्ति। (बालक मित्रों के साथ खेलते हैं।)
3. नमः – गुरवे नमः। (गुरु के लिए नमस्कार है।)
4. क्रुध् – दुर्जनः सज्जनाय क्रुध्यति। (दुष्ट व्यक्ति सज्जन पर क्रोध करता है।)
पिता पुत्राय क्रुध्यति। (पिता पुत्र पर क्रोध करता है।)

प्रत्ययाधारित वाक्य निर्माणम्

1. पठित्वा – छात्रः अत्र पठित्वा गच्छति। (छात्र यहाँ पढ़कर जाता है।)
2. गत्वा – छात्रः विद्यालयं गत्वा पठति। (छात्र विद्यालय जाकर पढ़ता है।)
3. आगत्य – रामः अत्र आगत्य पठति। (राम यहाँ आकर पढ़ता है।)
4. प्रणम्य – सेवकः प्रणम्य अवदत्। (सेवक प्रणाम करके बोला।)

पदाधारित वाक्य निर्माणम्

1. आसन् – बालकाः कक्षायाम् आसन्। (बालक कक्षा में थे।)
2. कुर्वन्ति – छात्राः गृहकार्यं कुर्वन्ति। (छात्र गृहकार्य करते हैं।)
3. अपतत् – सोहनः अश्वात् अपतत्। (सोहन घोड़े से गिर पड़ा।)
4. गच्छताम् – तौ गृहं गच्छताम्। (वे दोनों घर जावें।)

अभ्यासः

प्रश्न 1.
अधोलिखितशब्दानां सहायतया वाक्यनिर्माणं कुरुत-(निम्न शब्दों की सहायता से वाक्य-निर्माण कोजिए।)
[जीवितम्, शरणम्, दशनैः, निर्मलम्, करणीयम्, भृशम्, नगरात्, कान्तारे, क्षणमपि, कलरवः, जनेभ्यः, वनप्रदेशम्।]
उत्तरम् :
जीवितम् – प्रदूषितपर्यावरणे जीवितं कठिनं जातम्। (प्रदूषित पर्यावरण में जीवन कठिन हो गया है।)
शरणम् – श्रीकृष्णः शरणं मम। (श्रीकृष्ण मेरे आश्रय हैं।)
दशनैः – मानवः दशनैः भोजनं खादति। (मनुष्य दाँतों से खाना खाता है।)
निर्मलम् – निर्मलम् एव जलं पिबेत्। (शुद्ध जल ही पीना चाहिए।)
करणीयम् – कर्त्तव्यम् एव करणीयम्। (करने योग्य कार्य करना चाहिए।)
भृशम् – अद्य जलं भृशं दूषितम्। (आज पानी बहुत प्रदूषित है।)
नगरात – नगरात बहिरेव एकम् उद्यानम् अस्ति। (नगर के बाहर ही एक बाग है।)
कान्तारे – सीता निर्जनकान्तारे रामेण सह अगच्छत्। (सीता निर्जन वन में राम के साथ गई।)
क्षणमपि – न कश्चित् क्षणमपि तिष्ठति अकर्मकृत्। (कोई क्षणभर भी बिना काम किए नहीं रहता।)
कलरवः – खगानां कलरवः अतिमनोहरः भवति। (पक्षियों का कलरव मनोहर होता है।)
जनेभ्यः – स्वस्ति स्यात् जगतां जनेभ्यः। (संसार के लोगों का कल्याण हो।)
वनदेशम् – पशवः प्रातरेव वनप्रदेशं गच्छन्ति। (पशु प्रातः ही वन प्रदेश को जाते हैं।)

प्रश्न 2.
अधोलिखितानां पदानां सहायतया वाक्यनिर्माणं कुरुत-(निम्नलिखित शब्दों की सहायता से वाक्य बनाइए-)
[विमुक्ता, पितुहम्, दृष्ट्वा]
उत्तरम् :
विमुक्ता – सा व्याघ्रमारी निजबुद्ध्या व्याघ्रभयाद् विमुक्ता। (वह व्याघ्रमारी अपनी बुद्धि से बाघ के भय से मुक्त हो गई।)
पितुर्ग्रहम् – नार्यः रक्षाबन्धनोत्सवे पितुर्गृहं गच्छन्ति। (स्त्रियाँ रक्षाबन्धन के त्यौहार पर पिता के घर जाती हैं।)
दृष्ट्वा – सिंह दृष्ट्वा भयाद् असौ पलायितवान्। (सिंह को देखकर डर से वह भाग गया।)

प्रश्न 3.
अधोलिखितशब्दानां सहायतया वाक्यानां निर्माणं कुरुत- (निम्नलिखित शब्दों की सहायता से वाक्य का निर्माण कीजिए)-
[कृत्वा, सुखम्, समन्ततः, गात्राणाम्, लाघवम्, सुविभक्तता, आरोग्य, परमम्, पिपासा, सहसा]
उत्तरम् :
कृत्वा – सा गृहकार्यं कृत्वा विद्यालयं गच्छति। (वह गृहकार्य करके विद्यालय को जाती है।)
सुखम् – यावत् जीवेत् सुखं जीवेत्। (जब तक जीओ सुख से जीओ।)
समन्ततः – जनाः समन्ततः तत्र आगताः (लोग सभी ओर से वहाँ आ गये।)
गात्राणाम् – गात्राणाम् अनीशोऽहमस्मि। (मैं अपने अंगों का भी स्वामी नहीं हूँ।)
लाघवम् – मनुष्यः प्रयत्नलाघवम् अनुसरति। (मनुष्य प्रयत्न लाघव का अनुसरण करता है। )
सुविभक्तता – गात्राणाम् अपि सुविभक्तता शोभते। (अंगों का सुन्दर विभाजन शोभा देता है।)
आरोग्यम् – आरोग्यं परमं सुखम्। (नीरोग होना सबसे बड़ा सुख है।)
परमम् – दारिद्रयं परमापदां पदम्। (दरिद्रता महान आपदाओं का स्थान है।)
पिपासा – ग्रीष्मे पिपासा अतिबाधते। (गर्मियों में प्यास अधिक कष्ट देती है।)
सहसा – सहसा विदधीत न क्रियाम्। (अकस्मात् कोई काम नहीं करना चाहिए।)

प्रश्न 4.
अधोलिखितशब्दानां सहायतया वाक्यनिर्माणं कुरुत – (निम्नलिखित शब्दों की सहायता से वाक्य-निमाण कीजिए-)
[उपसृत्य, अलम्, लालनीयः, खलु, नामधेयम्, धिक, अपूर्वः, श्लाघ्या, त्वरयति।]
उत्तरम् :
उपसृत्य – रामः जनकम् उपसृत्य प्रणमति। (राम पिता के पास जाकर प्रणाम करता है।)
अलम् – अलं विवादेन। (विवाद मत करो।)
लालनीयः – शिशु पित्रोः लालनीयः भवति। (बच्चा पिता का लाडला होता है।)
खलु – मा खलु चापलं कुरु। (निश्चित ही चपलता मत करो !)
नामधेयम् – किं ते नामधेयम् ? (तेरा क्या नाम है ?)
धिक् – धिक् त्वाम्। (तुझे धिक्कार है।)
अपूर्वः – अपूर्वः कोऽपि कोशोऽयं विद्यते तव भारती। (हे सरस्वती ! यह तुम्हारा खजाना अनोखा है।)
श्लाघ्या – श्लाघ्या इयं रामायणी कथा। (यह रामायण की कथा सराहनीय है।)
त्वरयति – श्रमस्य फलं मां त्वरयति। (श्रम का फल मुझसे जल्दी करवा रहा है।)

प्रश्न 5.
अधोलिखित पदानां सहायताया वाक्य निर्माणं कुरुत। (निम्न पदों से वाक्य बनाइये)
[हलमा पपात, जवन, कषावल, वषभ, भारम, धेनूनाम्, अश्रूणि, वासवः, बोदुम्।]
उत्तरम् :
हलम् – वृषभौ हलम् स्कन्धो धृत्वा क्षेत्रं गच्छतः। (बैल हल लेकर खेत पर जाते हैं।)
पपात – एकं पाषाण खण्डं उपरितः पपात तेन सः हतः। (एक पत्थर का टुकड़ा ऊपर से गिरा, जिससे वह मर गया।)
जवेन – सः जवेन गच्छति एव, मार्गेऽहं मिलितवान्। (वह तेज गति से जा ही रहा था कि रास्ते में मैं मिल गया)
कृषीवलः – कृषीवल: अन्नमुत्पादयति। (किसान अन्न पैदा करता है।)
वृषभः – वृषभः कृषिकार्ये कृषकस्य सदैव सहायतां करोति। (बैल खेती के काम में किसान की सदैव सहायता करता है।)
भारम् – निर्बलः जनः भारम् न सोढुं शक्नोति। (निर्बल व्यक्ति भार नहीं ढो सकता।)
धेनूनाम् – सर्वासां धेनूनाम् जननी सुरभिः। (सभी गायों की माता सुरभि है।)
अश्रूणि – तस्य नेत्राभ्याम् अश्रूणि पतन्ति। (उसकी आँखों से आँसू गिरते हैं।)
वासवः – इन्द्रः वासवः इति नाम्नानि ख्यातः। (इन्द्र वासव के नाम से भी प्रसिद्ध हैं।)
बोढुम् – स्वस्थ मनुष्य एव भारं बोढुं शक्नोति। (स्वस्थ मनुष्य ही बोझा ढो सकता है।)

प्रश्न 6.
अधोलिखितपदानां सहायतया वाक्यनिर्माणं कुरुत (निम्नलिखित पदों की सहायता से वाक्य बनाइए)
उत्तरम् :
महान् – सुभाषः महान् पुरुषः आसीत्। (सुभाष महान् पुरुष था।)
समः – न कोऽपि वीरः रामेण समः। (राम के समान कोई वीर नहीं।)
कृत्वा – बालकः गृहकार्यं कृत्वा विद्यालयं गच्छति। (बालक गृहकार्य करके विद्यालय जाता है।)
ध्रुवम् – ध्रुवम् एव सः आयास्यति। (निश्चित ही वह आयेगा।)
अपगमे – मेघजालस्यापगमे चन्द्रः दृश्यते। (मेघजाल के हट जाने पर चन्द्रमा दिखाई पड़ता है।)
निमित्तम् – मूर्खाः किमपि निमित्तं विधाय कलहं कुर्वन्ति। (मूर्ख कोई कारण रखकर झगड़ा करते हैं।)
प्रथमः – पुस्तके प्रथमः पाठः मङ्गलाचरणं भवति। (पुस्तक में पहला पाठ मंगलाचरण होता है।)
यथा – यथा वृष्टिः भवति तथैव जलं प्रवहति। (जैसे वर्षा होती है वैसे ही जल बहता है।)
एव – माम् सः एव जानाति। (मुझे वह ही जानता है।)
सेवितव्यः – आचार्यः सर्वतोभावेन सेवितव्यः। (आचार्य की पूर्ण रूप से सेवा करनी चाहिए।)

प्रश्न 7.
अधोलिखित पदानां सहायतया वाक्य निर्माणं कुरुत – (निम्न पदों की सहायता से वाक्य निर्माण कीजिए।)
[समीपे, प्रहर्तुम्, आरूढः, आकृष्य, तुदन्ति, गर्जति, इतस्ततः, सन्नपि, जायते, किमर्थम्।]
उत्तरम् :
समीपे – समीपे एव उद्यानमस्ति यत्र वयं भ्रमामः। (पास में एक उद्यान है जहाँ हम घूमते हैं।)
प्रहर्तुम् – चौरः गृहस्वामिनः उपरि प्रहर्तुम् ऐच्छत। (चोर ने गृहस्वामी पर प्रहार करना चाहा।)
आरूढः – रथम् आरूढ़ः अर्जुनः शत्रून हन्ति। (रथ पर चढ़ता हुआ अर्जुन शत्रुओं को मारता है।)
आकृष्य – वानरः सिंहस्य कर्णमाकृष्य वृक्षमारोहति। (वानर सिंह का कान खींचकर पेड़ पर चढ़ जाता है।)
तुदन्ति – किमर्थं मामेव तुदन्ति सर्वे मिलित्वा। (तुम सभी मिलकर क्यों तंग कर रहे हो?)
गर्जति – सिंहः उच्चैः गर्जति। (सिंह जोर से दहाड़ता है।)
इतस्ततः – वानरं दृष्ट्वा बालकः इतस्ततः धावन्ति। (बन्दर को देखकर बालक इधर-उधर दौड़ते हैं।)
सन्नपि – सिंह सन्नपि वानरेभ्य विभेति। (शेर होते हुए भी वानरों से डरते हो।)
जायते – कामात् जायते क्रोधः। (काम से क्रोध पैदा होता है।)
किमर्थम् – त्वं किमर्थम् अत्र आगतोऽसि? (तुम यहाँ किसलिए आये हो?)

प्रश्न 8.
अधोलिखितानां पदानां सहायतया वाक्यनिर्माणं कुरुत – (निम्नलिखित पदों की सहायता से वाक्य बनाइये।)
उत्तरम् :
भूरि – सः निर्धनेभ्यः भूरि धनमयच्छत्। (उसने निर्धनों के लिए बहुत-सा धन दिया।)
संलग्नः – साधुः स्वकार्ये संलग्नः अभवत् (साधु अपने काम में लग गया।)
विचार्य – किञ्चित् विचार्य सोऽवदत्। (कछ विचार कर वह बोला।)
उपस्थातुम् – अंहं विद्यालये उपस्थातुम् असमर्थोऽस्मि। (मैं विद्यालय में उपस्थित होने में असमर्थ हूँ।)
अन्येधुः – अन्येधुः सः विदेशं गतवान्। (दूसरे दिन वह विदेश चला गया।)
निकषा – ग्रामं निकषा पाठशाला अस्ति। (गाँव के पास पाठशाला है।)।
वक्तुम् – अपि किमपि वक्तुम् इच्छति भवान्। (क्या आप कुछ कहना चाहते हैं ?)
अध्वनि – स: मां अध्वनि सर्वम् एव वृत्तम् अकथयत्। (उसने मुझसे मार्ग में सारा वृत्तान्त कह दिया।)
भुक्ष्व – भुक्ष्व इदानी स्वकर्मणः फलम्। (भोग अब अपने कर्म का फल।)

प्रश्न 9.
अधोलिखित शब्दानां सहायतया वाक्य निर्माणं कुरुत –
(निम्नलिखित शब्दों की सहायता से वाक्य निर्माण कीजिये।)
[यच्छति, विद्याधनम्, चित्ते, वाचि, त्यक्त्वा, पक्वं, वदने, प्रोक्तम्, परिभूयते, आत्मनः]
उत्तरम् :
यच्छति – धनिकः भिक्षुकेभ्यः भोजनं यच्छति। (धनवान भिक्षुओं को भोजन देता है।)
विद्याधनम् – विद्याधनं सर्वधन प्रधानम्। (विद्याधन सभी धनों में प्रमुख है।)
चित्ते – न चित्ते केभ्यः अपि अहितभावः भवेत्। (मन में किसी के लिये अहित का भाव न हो।)
वाचि – वाचि सत्यम् भवेत्। (वाणी में सत्यता होनी चाहिये।)
त्यक्त्वा – परपीडनं त्यक्त्वा सदैव परोपकारमेव कुर्यात्। (दूसरों को दुख देने को त्यागकर परोपकार करना चाहिये।)
पक्वं – पक्वमेव फलं मधुरं भवति। (पका हुआ फल ही मीठा होता है।)
वदने – तस्य वदने स्मिति तस्य प्रसन्नतां दर्शयिति। (उसके मुँह पर मुस्कराहट उसकी प्रसन्नता को दर्शाती है।)
प्रोक्तम् – इति महापुरुषैः प्रोक्तम्। (ऐसा महापुरुषों ने कहा)
परिभूयते – मूर्खः सर्वत्रैव परिभूयते। (मूर्ख सब जगह अपमानित किया जाता है।)
आत्मनः – आत्मनः हितचिन्तनमेव स्वार्थम्। (अपना हित सोचना ही स्वार्थ है।)

प्रश्न 10.
अधोलिखितानां पदानां सहायतया वाक्यनिर्माणं कुरुत।
(निम्नलिखित पदों की सहायता से वाक्य-निर्माण कीजिए।)
[जातम्, अकस्मात्, बहुभूमिकानि, महत्कम्पनम्, भीषणम्, विभीषिका, खलु, वस्तुतः, निर्माय।]
उत्तरम् :
जातम् – स्वातन्त्र्यं प्राप्य भारतं राष्ट्र प्रसन्नं जातम्। (स्वतन्त्रता प्राप्त करके भारत राष्ट्र प्रसन्न हो गया।)
अकस्मात् – अकस्मात् एव युद्धस्य स्थितिः उपस्थिता। (अचानक ही युद्ध की स्थिति उपस्थित हो गई।)
बहुभूमिकानि – महानगरेषु बहुभूमिकानि भवनानि सन्ति। (महानगरों में बहुमंजिले भवन हैं।)
महत्कम्पनम् – भूकम्पे जाते धरायाः महत् कम्पनम् आरभते। (भूकम्प आने पर धरती का अत्यन्त काँपना आरम्भ होता है।)
भीषणम् – कौरवपाण्डवयोः भीषणं युद्धम् अजायत। (कौरव-पाण्डवों का भीषण युद्ध हुआ।)
विभीषिका – भूकम्पस्य विभीषिका युद्धाद् अपि भयङ्करा। (भूकम्प की आपदा युद्ध से भी अधिक भयंकर है।)
खलु – मा खलु चापलं कुरु। (निश्चय ही चपलता मत करो।)
वस्तुतः – वस्तुतः प्रदूषणम् एव रोगाणां कारणम्। (वास्तव में प्रदूषण ही रोगों का कारण है।)
निर्माय – खगाः अपि नीडं निर्माय निवसन्ति। (पक्षी भी घोंसला बनाकर निवास करते हैं।)

प्रश्न 11.
अधोलिखितानां पदानां सहायतया वाक्य-निर्माणं कुरुत – (निम्नलिखित शब्दों की सहायता से वाक्य बनाइये)
[द्रष्टुम्, निष्क्रम्य, प्रविश्य, पिधाय, भवान्, रक्षसि, क्व, ज्ञायते, दुष्करम्।]
उत्तरम् :
द्रष्टुम् – बालकः चलचित्रं द्रष्टुम् इच्छति। (बालक चलचित्र देखना चाहता है।)
निष्क्रम्य – मूषक: बिलात् निष्क्रम्य भूमौ लुण्ठति। (चूहा बिल से निकलकर धरती पर लोटता है।)
प्रविश्य – सा कक्षां प्रविश्य आचार्यां नमति। (वह कक्षा में प्रवेश करके आचार्या को नमस्कार करती है।)
पिधाय – धनिकः कुम्भं पिधाय भूमौ निक्षिप्तवान्। (धनवान् ने घड़े को ढंककर धरती में रख दिया।)
भवान् – भवान् कुत्र गच्छति ? (आप कहाँ जा रहे हैं ?)
रक्षसि – हे ईश्वर ! त्वं सर्वान् रक्षसि। (हे ईश्वर ! तू सबकी रक्षा करता है।)
क्व – इदानीं सः धूर्तः क्व गतः ? (अब वह चालाक कहाँ गया ?)
ज्ञायते – सर्वमिदं मया ज्ञायते। (यह सब मुझे ज्ञात है।)
दुष्करम् – कः कुर्यात् इदं दुष्करं शिविना विना ? (शिवि के बिना इस दुष्कर कार्य को और कौन करे!)

प्रश्न 12.
अधोलिखितानां शब्दानां सहायतया वाक्यनिर्माणं कुरुत – (निम्नलिखित शब्दों की सहायता से वाक्य बनाइये।)
उत्तरम् :
भुक्तम् – तेन भोजनं भुक्तम्। (उसने खाना खाया।)
निपीतम् – मया भोजनान्ते तक्रं निपीतम्। (मैंने भोजन के बाद छाछ पी है।)
वद – सत्यं वद। (सत्य बोल।)
परितः – ग्रामं परितः राजमार्गः। (गाँव के चारों ओर सड़क है।)
रसालमुकुलानि – भ्रमराः वसन्तकाले रसालमुकुलानि आश्रयन्ते। (भौरे वसन्तकाल में आम के बौर का आश्रय लेते हैं।)
हन्त – हन्त ! अनेके वीराः हताः युद्धे। (खेद है, अनेक वीर युद्ध में मारे गये।)
पूरयित्वा – वारिदः जलाशयान् पूरयित्वा रिक्तः भवति। (बादल जलाशयों को भरकर खाली हो जाता है।)
काननानि – सीता लक्ष्मणेन सह काननानि द्रष्टुम् अगच्छत्। (सीता लक्ष्मण के साथ जंगलों को देखने गई।)
जलदः – जलदः वर्षति जलं च प्रवहति। (बादल बरसता है और पानी बहता है।)

Jharkhand Board JAC Class 9 Maths Solutions Chapter 8 Quadrilaterals Ex 8.1 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions Chapter 8 Quadrilaterals Ex 8.1

Page-146

Question 1.
The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Answer:
Let the angles be 3x, 5x, 9x and 13x.
Sum of the interior angles of the quadrilateral = 360°
Now, 3x + 5x + 9x + 13x = 360°
⇒ 30x = 360°
⇒ x = 12°
Angles of the quadrilateral are:
3x = 3 × 12° = 36°
5x = 5 × 12° = 60°
9x = 9 × 12° = 108°
13x= 13 × 12°= 156°

Question 2.
If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Answer:
Given: AC = BD
To prove: ABCD is a rectangle.
Proof: In order to prove ABCD is a rectangle we need to prove that one of its interior angle is right angle.
In ΔABD and ΔBAD,
BA = BA (Common)
BC = AD (Opposite sides of a parallelogram are equal)
AC = BD (Given)
Therefore, ΔABC = ΔBAD by SSS congruence criterion.
⇒ ∠A = ∠B (by CPCT)
Also, ∠A + ∠B = 180° (Sum of the angles on the same side of the transversal)
⇒ 2∠A = 180°
⇒ ∠A = 90° = ∠B
Thus, ABCD is a rectangle.

Question 3.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Answer:
Let ABCD be a quadrilateral whose diagonals bisect each other at right angles.
Given: OA = OC, OB = OD and ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
To prove: ABCD is parallelogram and AB = BC = CD = AD
Proof: In ΔAOB and ΔCOB,
OA = OC
∠AOB = ∠COB = 90°
OB = OB (Common)
Therefore, ΔAOB ≅ ΔBOC by SAS congruence criterion.
Thus, AB = BC (by CPCT)
Similarly, we can prove,
AB = BC = CD = AD Opposites sides of a quadrilateral are equal hence ABCD is a parallelogram.
Thus, ABCD is rhombus.

Question 4.
Show that the diagonals of a square are equal and bisect each other at right angles.

Answer:
Given: Let ABCD be a square and its diagonals AC and BD intersect each other at O.
To prove: AC = BD, AO = OC and ∠AOB = 90°
Proof: In ΔABC and ΔBAD,
AB = BA (Common)
∠ABC = ∠BAD = 90° (Each angle of square is of 90°)
BC = AD (All sides of square are equal)
Therefore, ΔABC ≅ ΔBAD by SAS congruence criterion.
Thus, AC = BD (by CPCT).
i.e., diagonals are equal.

Now, In ΔAOB and ΔCOD,
∠BAO = ∠DCO (Alternate interior angles)
∠AOB = ∠COD (Vertically opposite angles)
AB = CD (Given)
Therefore, ΔAOB = ΔCOD by AAS congruence criterion.
Thus, AO = CO and BO = DO by CPCT i.e.
Diagonals bisect each other.
Now, In ΔAOB and ΔCOB,
OB = OB (common)
AO = CO (Proved above)
AB = CB (Sides of the square)
Therefore, ΔAOB ≅ ΔCOB by SSS congruence criterion.
∴ ∠AOB = ∠COB (CPCT)
Also, ∠AOB + ∠COB = 180°
(Linear pair)
Thus, ∠AOB = ∠COB = 90° i.e.
Diagonals bisect each other at right angles.

Question 5.
Show that if the diagonals of a which diagonals AC and BD bisect each other at right angles at O.

Answer:
Given: Let ABCD be a quadrilateral in which diagonals AC and BD bisect each other at right angles at O.
To prove: Quadrilateral ABCD is a square.
Proof: In ΔAOB and ΔCOD,
AO = CO (Diagonals bisect each other)
∠AOB = ∠COD (Vertically opposite angles)
OB = OD (Diagonals bisect each other)
Therefore, ΔAOB ≅ ΔCOD by SAS congruence criterion.
Thus, AB = CD by CPCT. ……. (i)
Now, In ΔAOD and ΔCOD,
AO = CO (Diagonals bisect each other)
∠AOD = ∠COD = 90° (Diagonals bisect each other at right angle)
OD = OD (Common)
Therefore, ΔAOD ≅ ΔCOD by SAS congruence criterion.
Thus, AD = CD by CPCT
Similarly, ΔCOD ≅ ΔBOC and BC = CD (CPCT)
⇒ AD = BC = CD = AB ……… (ii)
Also, as diagonals bisect each other, so, ABCD is a parallelogram.

Consider ΔACD and ΔBDC
AD = BC (Proved above)
CD = CD (Common)
AC = BD (Given)
⇒ ΔACD ≅ ΔBDC (by SSS congruence criterion)
⇒ ∠ADC = ∠BCD (CPCT)
As ABCD is a parallelogram so,
AD || BC
⇒ ∠ADC + ∠BDC = 180° (Angles on the same side of transversal)
∴ ∠ADC – ∠BCD = 90°.
So, ABCD is a parallelogram in which all sides are equal and one angle is 90°
⇒ ABCD is a square.

Question 6.
Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig.). Show that
(i) it bisects ∠C also,
(ii) ABCD is a rhombus.

Answer:
(i) As ABCD is a parallelogram
⇒ AB || CD and AD || BC
⇒ ∠BAC = ∠ACD …….(i)
(Alternate interior angles)
∠CAD = ∠ACB ……. (ii)
(Alternate interior angles)
Also, ∠CAD = ABAC …….. (iii)
(As AC bisects ∠A)
Therefore, ∠BCA=∠DCA [By (i), (ii), (iii)]
⇒ AC bisects ∠C.

(ii) As ABCD is a parallelogram
⇒ AD = BC and AB = CD …(iv)
Also, as ∠CAD = ∠ACB (Alternate interior angles)
and ∠ACB = ∠ACD (Proved)
⇒ ∠CAD = ∠ACD
⇒ AD = CD …(v)
(sides opposites to equal angles are equal)
Similarly, AB = BC …(vi)
Therefore, AB = BC = CD = AD (By (iv), (v) (vi))
So, ABCD is a parallelogram in which all sides are equal.
⇒ ABCD is a rhombus.

Question 7.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and

Answer:
Let ABCD is a rhombus and AC and BD be its diagonals.
Proof: In ΔACD – AD = CD (Sides of a rhombus)
∠DAC = ∠DCA
(Angles opposite to equal sides of a triangle are equal)
Also, AB || CD (Opposite sides of rhombus are parallel)
⇒ ∠DAC = ∠BCA (Alternate interior angles)
⇒ ∠DCA = ∠BCA
Therefore, AC bisects ∠C.
In ∆ABC,
AB = BC (Sides of a rhombus)
⇒ ∠BAC = ∠BCA (Angles opposite to equal sides are equal)
Also, AD || BC (Opposite sides of rhombus are parallel)
⇒ ∠DAC = ∠BCA (Alternate interior angles)
∴ ∠BAC = ∠DAC
⇒ AC bisects ∠A
Similarly we can prove that diagonal BD bisects ∠B as well as ∠D.

Question 8.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:
(i) ABCD is a square
(ii) diagonal BD bisects ∠B as well as ∠D.

Answer:
(i) AB || CD and AD || BC (∵ opposite sides of rectangle are parallel)
⇒ ∠1 = ∠4 and∠2=∠3 (Alternate interior angles)
Also, as AC bisects ∠A and ∠C
⇒ ∠1 = ∠2 and ∠3 = ∠4
Therefore ∠2 = ∠4
So, in ΔACD,
AD = CD (sides opposite to equal angles are equal)
Also, AD = BC and AB = CD (∵ opposite sides of rectangle are equal)
∴ AB = BC = CD = AD
⇒ ABCD is a rectangle in which all sides are equal
⇒ ABCD is a square.

(ii) In ΔABD,
AB = AD (sides of a square)
⇒ ∠5 = ∠7 (Angles opposite to equal sides are equal)
Also, as AB || CD
⇒ ∠5 = ∠8 (Alternate interior angles)
∴ ∠7 = ∠8
⇒ BD bisects ∠D
Similarly, BD bisects ∠B.

Page-147

Question 9.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig). Show that:

(i) ΔAPD ≅ ΔCQB
(ii) AP = CQ
(iii) ΔAQB ≅ ΔCPD
(iv) AQ = CP
(v) APCQ is a parallelogram
Answer:
(i) In ΔAPD and ΔCQB,
DP = BQ (Given)
∠ADP = ∠CBQ (Alternate interior angles)
AD = BC (Opposite sides of a ||^gm)
Thus, ΔAPD ≅ ΔCQB
(by SAS congruence criterion)

(ii) AP = CQ by CPCT as ΔAPD ≅ ΔCQB.

(iii) In ΔAQB and ΔCPD,
BQ = DP (Given)
∠ABQ = ∠CDP (Alternate interior angles)
AB = CD (Opposite sides of a ||^gm)
Thus, ΔAQB ≅ ΔCPD by SAS congruence criterion.

(iv) AQ = CP by CPCT as ΔAQB ≅ ΔCPD.

(v) From (ii) and (iv), we get opposite sides of quadrilateral APCQ are equal. Thus, APCQ is a ||^gm.

Question 10.
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ

Answer:
(i) In ΔAPB and ΔCQD,
∠ABP = ∠CDQ (Alternate interior angles)
∠APB = ∠CQD = 90° (∵ AP and CQ are perpendiculars)
AB = CD (Opposite sides of a is a parallelogram)
Thus, ΔAPB ≅ ΔCQD (by AAS congruence criterion)

(ii) AP = CQ by CPCT as ΔAPB ≅ ΔCQD.

Question 11.
In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig).
Show that
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ΔABC ≅ ΔDEF.

Answer:
(i) AB = DE and AB || DE (Given)
Thus, quadrilateral ABED is a parallelogram because a pair of opposite sides of a quadrilateral are equal and parallel to each other.

(ii) Again BC = EF and BC || EF.
Thus, quadrilateral BEFC is a parallelogram.

(iii) Since ABED and BEFC are parallelograms.
⇒ AD = BE and BE = CF
(Opposite sides of a parallelogram are equal)
Thus, AD = CF.
Also, AD || BE and BE || CF
(Opposite sides of a parallelogram are parallel)
Thus, AD || CF

(iv) AD and CF are opposite sides of quadrilateral ACFD which are equal and parallel to each other.
Thus, ACFD is a parallelogram.

(v) AC || DF and AC = DF because ACFD is a parallelogram.

(vi) In ∆ABC and ∆DEF,
AB = DE (Given)
BC = EF (Given)
AC = DF (Opposite sides of a parallelogram ACFD)
Thus, ∆ABC ≅ ∆DEF (by SSS congruence criterion)

Question 12.
ABCD is a trapezium in which AB || CD and AD = BC.
Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ΔABC ≅ ΔBAD
(iv) diagonal AC = diagonal BD

[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]
Answer:
Construction: Draw a line through C parallel to DA intersecting AB produced at E.
Proof:
(i) In quadrilateral ∆DCE
AE || CD (as AB || CD)
AD || CE (By construction)
∴ ∆DCE is a parallelogram as opposite sides are parallel
CE = AD (Opposite sides of a parallelogram)
AD = BC (Given)
Therefore, BC = CE
⇒ ∠CBE = ∠CEB
(Angles opposite to equal sides)
also, ∠A + ∠CBE = 180°
(Angles on the same side of transversal and ∠CBE = ∠CEB)
∠B + ∠CBE = 180° (Linear pair)
⇒ ∠A = ∠B

(ii) ∠A + ∠D = ∠B+ ∠C= 180° (Angles on the same side of transversal)
⇒ ∠A + ∠D = ∠A + ∠C (∵ ∠A = ∠B)
⇒ ∠D = ∠C

(iii) In ∆ABC and ∆BAD,
AB = AB (Common)
∠DAB = ∠CBA (Proved)
AD = BC (Given)
Thus, ∆ABC ≅ ∆BAD by SAS congruence criterion.

(iv) Diagonal AC = diagonal BD by CPCT as ∆ABC ≅ ∆BAD.

Jharkhand Board JAC Class 9 Maths Solutions Chapter 7 Triangles Ex 7.3 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions Chapter 7 Triangles Ex 7.3

Page-128

Question 1.
∆ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig). If AD is extended to intersect BC at P, show that

(i) ΔABD ≅ ΔACD
(ii) ΔABP ≅ ΔACP
(iii) AP bisects ∠A as well as ∠D.
(iv) AP is the perpendicular bisector of BC.
Answer:
Given: ΔABC and ΔDBC are two isosceles triangles.
Proof: (i) In ΔABD and ΔACD,
AD = AD (Common)
AB = AC (ΔABC is isosceles)
BD = CD (ΔDBC is isosceles)
Therefore, ΔABD ≅ ΔACD by SSS congruence criterion.

(ii) In ΔABP and ΔACP,
AP = AP (Common)
∠PAB = ∠PAC (ΔABD ≅ ΔACD so by CPCT)
AB = AC (ΔABC is isosceles)
Therefore, ΔABP ≅ ΔACP by SAS congruence criterion.

(iii) ∠PAB = ∠PAC by CPCT as ΔABD ≅ ΔACD.
AP bisects ∠A. ………..(i)
Also, in ΔBPD and ΔCPD,
PD = PD (Common)
BD = CD (ΔDBC is isosceles)
BP = CP (ΔABP ≅ ΔACP so by CPCT)
Therefore, ΔBPD ≅ ΔCPD by SSS congruence criterion.
Thus, ∠BDP = ∠CDP by CPCT. …(ii) By (i) and (ii) we can say that AP bisects ∠A as well as ∠D.

(iv) ∠BPD = ∠CPD (by CPCT as ΔBPD = ΔCPD)
and BP = CP …(hi)
Also, ∠BPD + ∠CPD = 180° (BC is a straight line)
⇒ 2∠BPD = 180°
⇒ ∠BPD = 90° …(iv)
From (i) and (ii),
AP is the perpendicular bisector of BC.

Question 2.
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects ∠A.

Answer:
Proof: (i) In ΔABD and ΔACD,
∠ADB – ∠ADC = 90°
AB = AC (Given)
AD = AD (Common)
Therefore, ΔABD ≅ ΔACD by RHS congruence criterion.
Now,
BD = CD (by CPCT)
Thus, AD bisects BC.

(ii) ∠BAD = ∠CAD (by CPCT)
Thus, AD bisects ∠A.

Question 3.
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see Fig). Show that:

(i) ΔABM ≅ ΔPQN
(ii) ΔABC ≅ ΔPQR
Answer:
Given: AB = PQ, BC = QR and AM = PN
Proof:
(i) \(\frac{1}{2}\) BC = BM and \(\frac{1}{2}\) QR = QN (AM and PN are medians)
BC = QR (Given)
⇒ \(\frac{1}{2}\) BC = \(\frac{1}{2}\) QR
⇒ BM = QN

In ΔABM and ΔPQN,
AM = PN (Given)
AB = PQ (Given)
BM = QN (Proved above)
Therefore, ΔABM ≅ ΔPQN by SSS congruence criterion.

(ii) In ΔABC and ΔPQR,
AB = PQ (Given)
∠ABC = ∠PQR
(AABM = APQN so by CPCT) BC = QR (Given)
Therefore, ΔABC ≅ ΔPQR by SAS congruence criterion.

Question 4.
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Ans. Given: BE and CF are two equal altitudes.
Proof: In ABEC and ACFB,
∠BEC = ∠CFB = 90° (Altitudes)
BC = CB (Common)
BE = CF (Given)
Therefore, ΔBEC ≅ ΔCFB by RHS congruence criterion.
Now,
∠C = ∠B (by CPCT)
Thus, AB = AC (sides opposite to the equal angles are equal.)
Therefore, ΔABC is isosceles.

Question 5.
ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.

Answer:
Given: AB = AC
Proof: In ΔABP and ΔACP,
AB = AC (Given)
AP = AP (Common)
Therefore, ΔABP ≅ ΔACP by RHS congruence criterion.
Thus, ∠B = ∠C (by CPCT)

Jharkhand Board JAC Class 9 Sanskrit Solutions Shemushi Chapter 2 स्वर्णकाकः Textbook Exercise Questions and Answers.

JAC Board Class 9th Sanskrit Solutions Shemushi Chapter 2 स्वर्णकाकः

JAC Class 9th Sanskrit स्वर्णकाकः Textbook Questions and Answers

1. (अ) एकपदेन उत्तरं लिखत-(एक शब्द में उत्तर लिखिए-)
(क) माता काम् आदिशत्? (माता ने किसको आदेश दिया?)
उत्तरम् :
पुत्रीम् (बेटी को)।

(ख) स्वर्ण-काकः कान् अखादत्? (सोने का कौवा किन्हें खा गया?)
उत्तरम् :
तण्डुलान् (चावलों को)।

(ग) प्रासादः कीदृशः वर्तते? (महल कैसा है?)
उत्तरम् :
स्वर्णमयः (सोने का)।

(घ) गृहमागत्य तया का समुद्घाटिता? (घर आकर उसने क्या खोली?)
उत्तरम् :
मञ्जूषा (पेटी)।

(ङ) लोभाविष्टा बालिका कीदृशीं मञ्जूषां नयति? (लोभी लड़की कैसी मंजूषा को ले जाती है?)
उत्तरम् :
वृहत्तमाम् (सबसे बड़ी को)।

(आ) अधोलिखितानां प्रश्नानाम् उत्तराणि संस्कृतभाषया लिखत – (निम्नलिखित प्रश्नों के उत्तर संस्कृत भाषा में लिखिए-)
(क) निर्धनायाः वृद्धायाः दुहिता कीदृशी आसीत् ? (निर्धन वृद्धा की पुत्री कैसी थी?)
उत्तरम् :
निर्धनायाः वृद्धायाः दुहिता विनम्रा मनोहरा चासीत्। (निर्धन वृद्धा की पुत्री विनम्र और मनोहर थी।)

(ख) बालिकया पूर्वं कीदृशः काकः न दृष्टमः आसीत्? (बालिका के द्वारा पहले कैसा कौआ नहीं देखा गया था?)
उत्तरम् :
बालिकया पूर्वं स्वर्णपक्षो रजतचञ्चुः स्वर्णकाकः न दृष्टः आसीत्।
(बालिका के द्वारा पहले सोने के पंखों वाला, चाँदी की चोंच वाला सुनहला कौआ नहीं देखा गया था।)

(ग) निर्धनायाः दुहिता मञ्जूषायां कानि अपश्यत्? (निर्धना की पुत्री ने मंजूषा में किन्हें देखा?)
उत्तरम् :
निर्धनायाः दुहिता मञ्जूषायां महार्हाणि हीरकाणि अपश्यत्। (निर्धन की पुत्री ने मंजूषा में महँगे हीरे देखे।)

(घ) बालिका किं दृष्ट्वा आश्चर्यचकिता जाता? (बालिका क्या देखकर आश्चर्यचकित हो गई?)
उत्तरम् :
बालिका वृक्षस्योपरि स्वर्णमयं प्रासादं दृष्ट्वा आश्चर्यचकिता जाता।
(बालिका वृक्ष के ऊपर सोने का महल देखकर आश्चर्यचकित हो गई।)

(ङ) गर्विता बालिका कीदृशं सोपानम् अयाचत् कीदृशं च प्राप्नोत्?
(घमण्डी बालिका ने कैसी सीढ़ी माँगी. और कैसी प्राप्त की?)
उत्तरम् :
गर्विता बालिका स्वर्णमयसोपानम् अयाचत् ताम्रमयं च प्राप्नोत्।
(घमण्डी बालिका ने सोने की सीढ़ी माँगी और ताँबे की प्राप्त की।)

2. (क) अधोलिखितानां शब्दानां विलोमपदं पाठात् चित्वा लिखत –
(निम्नलिखित शब्दों के विलोमपद पाठ से चुनकर लिखिए-)
(i) पश्चात् …………
(ii) हसितुम् …………
(ii) अधः …………
(iv) श्वेतः …………
(v) सूर्यास्तः …………
(vi) सुप्तः …………
उत्तरम् :
शब्दः – विलोमपदम्
(i) पश्चात् – पूर्वम्
(ii) अधः – उपरि
(iii) सूर्यास्तः – सूर्योदयः
(iv) हसितुम् – रोदितुम्
(v) श्वेतः – कृष्णः
(vi) सुप्तः – प्रबुद्धः

(ख) सन्धिं कुरुत (संधि करिए-)
(i) नि + अवसत् ………
(ii) सूर्य + उदयः ……….
(iii) वृक्षस्य + उपरि ……….
(iv) हि + अकारयत् ……….
(v) च + एकाकिनी ……….
(vi) इति + उक्त्वा ……….
(vii) प्रति + अवदत् ……….
(viii) प्र. + उक्तम् ……….
(ix) अत्र + एव ……….
(x) तत्र + उपस्थिता ……….
(xi) यथा + इच्छम् ……….
उत्तरम् :
(i) न्यवसत्
(ii) सूर्योदयः
(iii) वृक्षस्योपरि
(iv) ह्यकारयत्
(v) चैकाकिनी
(vi) इत्युक्त्वा
(vii) प्रत्यवदत्
(viii) प्रोक्तम्
(ix) अत्रैव
(x) तत्रोपस्थिता
(xi) यथेच्छम्।

3. स्थूलपदान्यधिकृत्य प्रश्ननिर्माणं कुरुत –
(मोटे छपे शब्दों को आधार बनाकर प्रश्न निर्माण कीजिए-)
(क) ग्रामे निर्धना स्त्री अवसत्। (गाँव में निर्धन स्त्री रहती थी।)
(ख) स्वर्णकाकं निवारयन्ती बालिका प्रार्थयत्। (सुनहले कौए को रोकती हुई बालिका ने प्रार्थना की।)
(ग) सूर्योदयात् पूर्वमेव बालिका तत्रोपस्थिता। (सूर्योदय से पूर्व ही बालिका वहाँ उपस्थित हो गई।)
(घ) बालिका निर्धनमातुः दुहिता आसीत्। (बालिका गरीब माता की पुत्री थी।)
(ङ) लुब्धा वृद्धा स्वर्णकाकस्य रहस्यमभिज्ञातवती। (लोभी वृद्धा सुनहले कौए के रहस्य को जान गई।)

प्रश्न:-
(क) ग्रामे का अवसत्? (गाँव में कौन रहती थी?)
(ख) कं निवारयन्ती बालिका प्रार्थयत्? (किसे रोकती हुई बालिका ने प्रार्थना की?)
(ग) कस्मात् पूर्वमेव बालिका तत्रोपस्थिता? (किससे पहले ही बालिका वहाँ उपस्थित हो गई?)
(घ) बालिका कस्याः दुहिता आसीत् ? (बालिका किसकी पुत्री थी?)
(ङ) लुब्धा वृद्धा कस्य रहस्यमभिज्ञातवती? (लोभी वृद्धा किसके रहस्य को जान गई?)

4. प्रकृति-प्रत्यय-संयोगं कुरुत-(प्रकृति-प्रत्यय का संयोग कीजिए)
(पाठात् चित्वा वा लिखत) अथवा पाठ में से छाँटकर लिखिए।
(क) वि + लोक् + ल्यप् – ……………….
(ख) नि + क्षिप् + ल्यप् – ………………..
(ग) आ + गम् + ल्यप् – ………………..
(घ) दृश् + क्त्वा – …………..
(ङ) शी + क्त्वा – ………………
(च) लघु + तमप् – …………..
उत्तर :
(क) विलोक्य
(ख) निक्षिप्य
(ग) आगम्य/आगत्य
(घ) दृष्ट्वा
(ङ) शयित्वा
(च) लघुतमम्

5. प्रकृतिप्रत्यय-विभागं कुरुत-(प्रकृति-प्रत्यय को अलग कीजिए)
(क) रोदितुम् – ……………
(ख) दृष्ट्वा – ……………
(ग) विलोक्य – ……………
(घ) निक्षिप्य – ……………
(ङ) आगत्य – ………………
(च) शयित्वा – ……………
(छ) लघुतमम् – ……………
उत्तर :
(क) रुद् + तुमुन्
(ख) दृश् + क्त्वा
(ग) वि + लोक् + ल्यप्
(घ) नि + क्षिप् + ल्यप्
(ङ) आ + गम् + ल्यप्
(च) शी + क्त्वा
(छ) लघु + तमप्

6. अधोलिखितानि कथनानि कः/का, कं/ काम् च कथयति –
(निम्नलिखित कथनों को कौन किससे कहता है-)

उत्तर :
क:/का – कं/काम्
(क) स्वर्णकाकः (सुनहला कौआ) – बालिकाम् (बालिका से)
(ख) निर्धना वृद्धा (निर्धन वृद्धा) – पुत्रीम् (पुत्री से)
(ग) निर्धना बालिका (निर्धन बालिका) स्वर्णकाकम् (सुनहले कौए से)
(घ) स्वर्णकाकः (सुनहला कौआ) – निर्धनां बालिकाम् (निर्धन बालिका से)
(ङ) गर्विता बालिका (घमण्डी बालिका) – स्वर्णकाकम् (सुनहले कौए से)

7. उदाहरणमनुसृत्य कोष्ठकगतेषु पदेषु पञ्चमीविभक्तेः प्रयोगं कृत्वा रिक्तस्थानानि पूरयत –
(उदाहरणानुसार कोष्ठक में दिये गये पदों में पंचमी विभक्ति का प्रयोग कर रिक्त-स्थानों की पूर्ति कीजिए-) यथा – मूषकः बिलाद् बहिः निर्गच्छति। (बिल)
(क) जनः ……………. बहिः आगच्छति। (ग्राम)
(ख) नद्यः …………….. निस्सरन्ति। (पर्वत)
(ग)……………. पत्राणि पतन्ति। (वृक्ष)
(घ) बालकः ……………. विभेति। (सिंह)
(ङ) ईश्वरः…………………त्रायते। (क्लेश)
(च) प्रभुः भक्तं ………….. निवारयति। (पाप)
उत्तर :
(क) ग्रामात्
(ख) पर्वतेभ्यः
(ग) वृक्षात्
(घ) सिंहात्
(ङ) क्लेशात्
(च) पापात्।

JAC Class 9th Sanskrit स्वर्णकाकः Important Questions and Answers

प्रश्न: 1.
ग्रामे का न्यवसत्? (गाँव में कौन रहती थी?)
उत्तरम् :
ग्रामे एका निर्धना वृद्धा स्त्री न्यवसत्। (गाँव में एक गरीब वृद्धा स्त्री रहती थी।)

प्रश्न: 2.
माता किम् अकरोत्? (माता ने क्या किया?)
उत्तरम् :
माता स्थाल्यां तण्डुलान् निक्षिप्य पुत्री तद्रक्षणाय आदिदेश। (माता ने थाली में चावलों को रखकर पुत्री को उनकी रक्षा करने का आदेश दिया।)

प्रश्न: 3.
किञ्चित् कालादनन्तरं किम् अभवत्? (कुछ समय पश्चात् क्या हुआ?)
उत्तरम् :
किञ्चित् कालादनन्तरम् एकः विचित्रः काकः समुड्डीय तामुपजगाम। (कुछ समय पश्चात् एक विचित्र कौआ उड़कर उसके पास आया।)

प्रश्न: 4.
बालिकया कीदृशः काकः पूर्वं न दृष्टः? (बालिका ने कैसा कौआ पहले नहीं देखा था?)
उत्तरम् :
बालिकया स्वर्णपक्षो रजतचञ्चुः स्वर्णकाकः पूर्वं न दृष्टः। (बालिका ने सोने के पंखों वाला चाँदी की चोंच वाला सुनहला कौआ पहले नहीं देखा था।) .

प्रश्न: 5.
बालिका काकं किं प्रार्थयत्? (बालिका ने कौए से क्या प्रार्थना की?)
उत्तरम् :
बालिका काकं प्रार्थयत्-तण्डुलान् मा भक्षय। मदीया माता अतीव निर्धना वर्तते। (बालिका ने कौए से प्रार्थना की-चावलों को मत खाओ। मेरी माता बहुत गरीब है।)

प्रश्न: 6.
किं विलोक्य बालिका रोदितुम् आरब्धा? (क्या देखकर ..लिका ने रोना प्रारम्भ कर दिया?)
उत्तरम् :
काकं तण्डुलान् खादन्तं हसन्तञ्च विलोक्य बालिका रोदितुम् आरब्धा। . (कौए को चावलों को खाते हुए और हँसते हुए देखकर बालिका ने रोना आरम्भ कर दिया।)

प्रश्न: 7.
बालिका (कन्या) ग्रामात बहिः कदा उपस्थिता? (बालिका गाँव से बाहर कब उपस्थित हो गई?)
उत्तरम् :
बालिका सूर्योदयात्पूर्वमेव ग्रामात् बहिः उपस्थिता। (बालिका सूर्योदय से पूर्व ही गाँव से बाहर उपस्थित हो गई।)

प्रश्न: 8.
बालिकां वृक्षस्य अधः दृष्ट्वा काकेन किं कथितम्? (वृक्ष के नीचे बालिका को देखकर कौए ने क्या कहा?)
उत्तरम् :
काकेन कथितम्-हं हो. बाले! त्वमागता, तिष्ठ, अहं त्वत्कृते सोपानमवतारयामि, तत्कथय स्वर्णमयं रजतमयमुत ताम्रमयं वा। (कौए ने कहा-अरे बालिके तुम आ गई, ठहरो, मैं तुम्हारे लिए सीढ़ी उतारता हूँ, तो कहो सोने की या चाँदी की अथवा ताँबे की।)

प्रश्न: 9.
सोपानविषये कन्या काकं किं प्रावोचत? (सीढी के विषय में बालिका ने कौए से क्या कहा?)
उत्तरम् :
कन्या काकं प्रावोचत्-अहं निर्धनमातुर्दुहिता अस्मि। ताम्रसोपानेनैव आगमिष्यामि। (बालिका ने कौए से कहा-मैं निर्धन माता की पुत्री हूँ। ताँबे की सीढ़ी से ही आऊँगी।)

प्रश्न: 10.
श्रान्तां कन्यां विलोक्य काकः किं प्राह? (कन्या को थकी हुई देखकर कौए नें क्या कहा?)
उत्तरम् :
कन्यां श्रान्तां विलोक्य काकः प्राह-पूर्वं लघुप्रातराशः क्रियताम्। (बालिका को थकी हुई देखकर कौआ बोला-पहले थोड़ा-सा सुबह का नाश्ता कर लो।)

प्रश्न: 11.
बालिका स्थाल्याविषये किं व्याजहार? (बालिका ने थाली के विषय में क्या कहा?)
उत्तरम् :
स्थाल्याविषये बालिका व्याजहार-ताम्रस्थाल्यामेवाहं निर्धना भोजनं करिष्यामि। (थाली के विषय में बालिका ने कहा-मैं गरीब हूँ, (इसलिए) ताँबे की थाली में ही भोजन करूँगी।)

प्रश्न: 12.
प्रातराशकाले कन्या कदा आश्चर्यचकिता जाता? (नाश्ते के समय बालिका कब आश्चर्यचकित हो गई?)
उत्तरम् :
कन्या तदा आश्चर्यचकिता सञ्जाता यदा स्वर्णकाकेन स्वर्णस्थाल्यां भोजनं परिवेषितम्। (बालिका तब आश्चर्यचकित हो गई जब सुनहले कौए ने सोने की थाली में भोजन परोसा।)

प्रश्न: 13.
अन्ते काकः किं ब्रूते? (अन्त में कौए ने क्या कहा?)
उत्तरम् :
अन्ते काक: ब्रूते-बालिके! अहम् इच्छामि यत् त्वं सर्वदा अत्रैव तिष्ठ परं तव माता एकाकिनी वर्तते। (अन्त में कौए ने कहा-बालिका! मैं चाहता हूँ कि तुम हमेशा यहीं पर ठहरो लेकिन तुम्हारी माँ अकेली है।)

प्रश्न: 14.
काकः कक्षाभ्यन्तरात् किम् आनयत्? (कौआ कमरे के अन्दर से क्या लाया?)
उत्तरम् :
काकः कक्षाभ्यन्तरात् तिस्रः मञ्जूषाः आनयत्। (कौआ कमरे के अन्दर से तीन सन्दूकें लाया।)

प्रश्न: 15.
मञ्जूषाः निस्सार्य काकः बालिकां किम् अवदत्? (सन्दूकें निकालकर कौए ने बालिका से क्या कहा?)
उत्तरम् :
काकः बालिकाम् अवदत्-बालिके! यथेच्छं गृहाण मञ्जूषामेकाम्। (कौआ बालिका से बोला-बालिका! इच्छानुसार एक सन्दूक ग्रहण करो।)

प्रश्न: 16.
बालिका का मञ्जूषां गृहीतवती? (बालिका ने कौनसा सन्दूक लिया?)
उत्तरम् :
बालिका लघुतमां मञ्जूषां गृहीतवती। (बालिका ने सबसे छोटा सन्दूक लिया।)

प्रश्न: 17.
मञ्जूषां प्रगृह्य बालिकया किं कथितम्? (सन्दूक को लेकर बालिका ने क्या कहा?)
उत्तरम् :
मञ्जूषा प्रगृह्य बालिकया कथितम्-इयत् एव मदीयतण्डुलाना मूल्यम्। (सन्दूक लेकर बालिका ने कहा-इतना ही मेरे चावलों का मूल्य है।)

प्रश्न: 18.
मञ्जूषां समुद्घाट्य बालिका तस्यां किम् अपश्यत्? (सन्दूक को खोलकर बालिका ने उसमें क्या देखा?)
उत्तरम् :
मञ्जूषां समुद्घाट्य बालिका तस्यां महार्हाणि हीरकाणि अपश्यत्। (सन्दूक को खोलकर बालिका ने उसमें बहुमूल्य हीरों को देखा।)

प्रश्न: 19.
अपरा वृद्धा कस्य रहस्यम् अभिज्ञातवती? (दूसरी वृद्धा किसके रहस्य को जान गई?)
उत्तरम् :
अपरा वृद्धा स्वर्णकाकस्य रहस्यम् अभिज्ञातवती। (दूसरी वृद्धा सुनहले कौए के रहस्य को जान गई।)

प्रश्न: 20.
काकः निर्धनायै बालिकायै किं दातुम् अकथयत्? (कौए ने निर्धन बालिका के लिए क्या देने को कहा?)
उत्तरम् :
काकः निर्धनायै बालिकायै तण्डुलमूल्यं दातुम् अकथयत्। (कौए ने निर्धन बालिका के लिए चावलों का मूल्य देने को कहा।)

प्रश्न: 21.
निर्धना कन्या कीदृशं सोपानं अवतारयितुम् अकथयत्? (गरीब कन्या ने कैसी सीढ़ी उतारने को कहा?)
उत्तरम् :
निर्धना कन्या ताम्रसोपानम् अवतारयितुम् अकथयत्। (गरीब कन्या ने ताँबे की सीढ़ी उतारने को कहा।)

प्रश्न: 22.
निर्धनां बालिका काकः कति मञ्जूषाः ग्रहीतुम् अकथयत्? (कौए ने निर्धन बालिका से कितनी सन्दूकें लेने को कहा?)
उत्तरम् :
काकः निर्धनां बालिकाम् एकां मञ्जूषां ग्रहीतुम् अकथयत्। (कौए ने निर्धन बालिका से एक सन्दूक लेने को कहा।) ।

प्रश्न: 23.
लुब्धया बालिकया का मञ्जूषा गृहीता? (लोभी बालिका ने कौन-सी सन्दूक ग्रहण की?)
उत्तरम् :
लुब्धया बालिकया बृहत्तमा मञ्जूषा गृहीता। (लोभी बालिका ने सबसे बड़ी सन्दूक ग्रहण की।)

रेखांकित पदान्यधिकृत्य प्रश्न निर्माणं कुरुत-(रेखांकित पदों के आधार पर प्रश्न निर्माण करिए-)

प्रश्न: 1.
स्वर्णकाकः इति कथायां लोभस्य परिणामो वर्णितः। (स्वर्णकाकः कहानी में लोभ का परिणाम वर्णित है।)
उत्तरम् :
स्वर्णकाकः इति कथायां कस्य परिणामो वर्णित:? (इस कहानी में किसका परिणाम वर्णित है?)

प्रश्न: 2.
दुहिता विनम्रा मनोहरा चासीत्। (बेटी विनम्र और मनोहर थी।)
उत्तरम् :
दुहिता कीदृशी आसीत् ? (बेटी कैसी थी?)

प्रश्न: 3.
स्थाल्यां तण्डुलान् निक्षिप्य पुत्रीम् आदिशत्। (थाली में चावल रखकर बेटी को आदेश दिया।)
उत्तरम् :
स्थाल्यां कान् निक्षिप्य पुत्रीम् आदिशत्? (थाली में किन्हें रखकर बेटी को आदेश दिया।)

प्रश्न: 4.
बालिका रोदितुमारब्धा। (बालिका ने रोना आरम्भ किया।)
उत्तरम् :
का रोदितुमारब्धा? (किसने रोना आरम्भ किया?)

प्रश्नः 5.
सूर्योदयात्पूर्वमेव सा तत्रोपस्थिता। (सूर्योदय से पूर्व ही वह वहाँ उपस्थित हो गई।)
उत्तरम् :
सा तत्र कदा उपस्थिता? (वह वहाँ कब उपस्थित हुई?)

प्रश्न: 6.
सा स्वर्णसोपानेन स्वर्णभवनम् आरोहत। (वह सोने की सीढ़ी से स्वर्ण-भवन पर चढ़ी।)
उत्तरम् :
सा केन स्वर्णभवनम् आरोहत? (वह किससे सोने के भवन पर चढ़ी?)

प्रश्नः 7.
तदा सा आश्चर्यचकिता सजाता? (तब वह आश्चर्यचकित हो गई।)
उत्तरम् :
तदा सा कीदृशी सञ्जाता? (तब वह कैसी हो गई?)

प्रश्नः 8.
स्वर्णकाकेन स्वर्णस्थाल्यां भोजनं परिवेषितम्। (स्वर्ण काक द्वारा सोने की थाली में भोजन परोसा गया।)
उत्तरम् :
स्वर्णकाकेन कस्यां भोजनं परिवेषितम्? (स्वर्ण काक ने किसमें भोजन परोसा?)

प्रश्न: 9.
काकः कक्षाभ्यन्तरात् तिस्त्रः मञ्जूषा निस्सार्य अददात्। (कौए ने कमरे के अन्दर से तीन पेटी निकालकर दी।)
उत्तरम् :
काकः कुतः तिस्त्रः मञ्जूषा निस्सार्य अददात्। (कौए ने कहाँ से तीन पेटी निकालकर दी।)

प्रश्न: 10.
लुब्धया बालिकया लोभस्य फलं प्राप्तम्? (लोभी बालिका द्वारा लोभ का फल प्राप्त किया गया।)
उत्तरम् :
कया लोभस्य फलं प्राप्तम्? (किसके द्वारा लोभ का फल प्राप्त किया गया?)
कथाक्रम-संयोजनम् अधोलिखितवाक्यानि पठित्वा कथाक्रमसंयोजनं कुरुत (निम्नलिखित वाक्यों को पढ़कर कथा-क्रम-संयोजन कीजिए)

1. ईय॑या सा तस्य स्वर्णकाकस्य रहस्यमभिज्ञातवती।
2. तस्मिन्नेव ग्रामे एकाऽपरा लुब्धा वृद्धा न्यवसत्।
3. लघुतमा मञ्जूषां प्रगृह्य बालिकया कथितमियदेव मदीयतण्डुलानां मूल्यम्।
4. काकः प्राह-पूर्वं लघुप्रातराशः क्रियताम्।
5. भवने चित्रविचित्रवस्तूनि सज्जितानि दृष्ट्वा सा विस्मयं गता।
6. सूर्योदयात्पूर्वमेव सा तत्रोपस्थिता।
7. नैतादृशः स्वर्णपक्षो रजतचञ्चुः स्वर्णकाकस्तया पूर्वं दृष्टः।
8. तस्याश्चैका दुहिता विनम्रा मनोहरा चासीत्।

उत्तरम् :

1. तस्याश्चैका दुहिता विनम्रा मनोहरा चासीत्।
2. नैतादृशः स्वर्णपक्षो रजतचञ्चुः स्वर्णकाकस्तया पूर्वं दृष्टः।
3. सूर्योदयात्पूर्वमेव सा तत्रोपस्थिता।
4. भवने चित्रविचित्रवस्तूनि सज्जितानि दृष्ट्वा सा विस्मयं गता।
5. काकः प्राह-पूर्वं लघुप्रातराशः क्रियताम्।
6. लघुतमा मञ्जूषां प्रगृह्य बालिकया कथितमियदेव मदीयतण्डुलानां मूल्यम्।
7. तस्मिन्नेव ग्रामे एकाऽपरा लुब्धा वृद्धा न्यवसत्।
8. ईय॑या सा तस्य स्वर्णकाकस्य रहस्यमभिज्ञातवती।

भाषिक-विस्तार –

1. किसी भी काम को करके’ इस अर्थ में ‘क्त्वा’ प्रत्यय का प्रयोग किया जाता है। यथा-
पठित्वा – पठ् + क्त्वा = पढ़कर
गत्वा – गम् + क्त्वा = जाकर
खादित्वा – खाद् + क्त्वा = खाकर

इसी अर्थ में अगर धातु (क्रिया) से पहले उपसर्ग होता है तो ल्यप् प्रत्यय का प्रयोग होता है। धातु से पूर्व उपसर्ग होने की स्थिति में कभी भी ‘क्त्वा’ प्रत्यय नहीं हो सकता और उपसर्ग न होने की स्थिति में कभी भी ल्यप् प्रत्यय नहीं हो सकता है। यथा –

उप + गम् + ल्यप् = उपगम्य
सम् + पूज् + ल्यप् = सम्पूज्य
वि + विलोक्य आ + ल्यप् = आदाय
निर् + गम् + ल्यप् = निर्गत्य

2. प्रश्नवाचक शब्दों को अनिश्चयवाचक बनाने के लिए चित् और चन निपातों का प्रयोग किया जाता है। ये निपात जब सर्वनाम पदों के साथ लगते हैं तो सर्वनाम पद होते हैं और जब अव्यय पदों के साथ प्रयुक्त होते हैं तो अव्यय होते हैं।

यथा – कः = कौन
कः + चन = कश्चन = कोई
कः + चित् = कश्चित् = कोई
के + चन = केचन = कोई (बहुवचन में)
के + चित् = केचित् (बहुवचन में)
का + चन = काचन = कोई (स्त्री)
का + चित् = काचित् (कोई स्त्री)
काः + चन = काश्चन = कुछ स्त्रियाँ (बहुवचन में)
काः+ चित् = काश्चित् (कुछ स्त्रियाँ) (बहुवचन में)

“किम्’ शब्द के सभी वचनों, लिंगों व सभी विभक्तियों में ‘चित्’ और ‘चन’ का प्रयोग किया जा सकता है और उसे अनिश्चयवाचक बनाया जा सकता है।

जैसे- (i) किञ्चित्-प्रथमा में
(ii) केनचित्-तृतीया में
(iii) केषाञ्चित् (केषाम् + चित्)-षष्ठी में
(iv) कस्मिंश्चित्-सप्तमी में
(v) कस्याञ्चित्-सप्तमी (स्त्रीलिङ्ग में)

इस तरह ‘चित्’ के स्थान पर ‘चन’ का प्रयोग होता है। ‘चित्’ और ‘चन’ जब अव्यय पदों में लग जाते हैं तो वे अव्यय हो जाते हैं। जैसे- क्वचित्-क्वचन कदाचित्-कदाचन

3. संस्कृत में एक से चतुर् (चार) तक संख्यावाची शब्द पुल्लिङ्ग, स्त्रीलिङ्ग तथा नपुंसकलिङ्ग में अलग-अलग रूपों में होते हैं पर पञ्च (पाँच) से उनका रूप सभी लिङ्गों में एक-सा होता है।

स्वर्णकाकः Summary and Translation in Hindi

पाठ परिचयः – प्रस्तुत पाठ श्री पद्मशास्त्री द्वारा विरचित ‘विश्वकथाशतकम्’ नामक कथासंग्रह से लिया गया है। जिसमें विभिन्न देशों की सौ लोक कथाओं का संग्रह है। यह वर्मा देश की श्रेष्ठतम कथाओं में से एक है, जिसमें लोभ और उसके दुष्परिणामों के साथ-साथ त्याग और उसके सुपरिणामों का वर्णन एक ‘सुनहले पंखों वाले कौए’ के माध् यम से किया गया है।

प्राचीन समय में एक गाँव में एक वृद्ध स्त्री रहती थी। उसकी पुत्री विनम्र और सुन्दर थी। एक बार माता ने उससे धूप में रखे चावलों की पक्षियों से रक्षा करने को कहा। कुछ समय पश्चात् एक सुनहले पंखों वाला कौआ उड़ता हुआ वहाँ पहुँचा और चावलों को खाने लगा।

लड़की के मना करने पर उस कौए ने उस लड़की से सूर्योदय से पहले गाँव के बाहर पीपल के पेड़ के नीचे आकर चावलों का मूल्य लेने को कहा। जब सूर्योदय से पहले वह लड़की वहाँ पहुँची तो उस लड़की ने वृक्ष के ऊपर सोने का महल देखा। लड़की की त्याग-भावना से प्रसन्न हुए कौए ने उस लड़की को सोने की सीढ़ी से ऊपर चढ़ाया तथा सोने की थाली में स्वादिष्ट भोजन कराया। लड़की ने कौए द्वारा दी गयी तीन सन्दूकों में से सबसे छोटी सन्दूक को चावलों के मूल्य के रूप में स्वीकार किया। लड़की ने घर पहुँचकर सन्दूक को खोलकर देखा, उस सन्दूक में भरे हीरों को देखकर वह बहुत प्रसन्न हुई और वह उसी दिन से धनिक बन गई।

उसी गाँव की एक लालची स्त्री को जब उस निर्धन लड़की के धनिक बनने का पता चला तो उस लालची स्त्री ने भी अपनी पुत्री से धूप में रखे चावलों की पक्षियों से रक्षा करने को कहा। जब वह सुनहला कौआ वहाँ पहुँचकर चावलों को खाने लगा तो उस कौए को लड़की ने भी उन चावलों को खाने से रोका। कौए ने उस लड़की से भी सूर्योदय से पूर्व ! गाँव के बाहर पीपल के वृक्ष के नीचे आने को कहा। वह लड़की सूर्योदय से पहले वहाँ पहुँचकर कौए की निन्दा करने । लगी और चावलों का मूल्य माँगने लगी।

कौए द्वारा सीढ़ियों की पूछने पर अभिमानी लड़की बोली कि सोने की सीढ़ियों से आऊँगी, परन्तु ‘सुनहले पंखों वाले कौए’ ने उसके लिए ताँबे की सीढ़ी दी। कौए ने उस लड़की को भोजन भी ताम्रपात्र में कराया। कौए द्वारा दी गई तीन पेटियों में से सबसे बड़ी पेटी लेकर वह खुशी-खुशी घर लौटी और जब उस लड़की ने उस पेटी को खोलकर देखा तो भयंकर काले साँप के रूप में अपने लोभ के फल को प्राप्त कर दुःखी हुई। इसके पश्चात् उसने लालच करना छोड़ दिया।

मूलपाठः, शब्दार्थाः, सप्रसंग हिन्दी-अनुवादः, सप्रसंग संस्कृत-व्यारव्याः अवबोधन कार्यम् च । __ 1. पुरा कस्मिंश्चिद् ग्रामे एका निर्धना वृद्धा स्त्री न्यवसत्। तस्याः च एका दुहिता विनम्रा मनोहरा चासीत्। एकदा माता स्थाल्यां तण्डुलान् निक्षिप्य पुत्रीम् आदिशत्। “सूर्यातपे तण्डुलान् खगेभ्यो रक्षा” किञ्चित् कालादनन्तरम् एको विचित्रः काकः समुड्डीय तस्याः समीपम् अगच्छत्।

नैतादृशः स्वर्णपक्षो रजतचञ्चुः स्वर्णकाकस्तया पूर्वं दृष्टः। तं तण्डुलान् खादन्तं हसन्तञ्च विलोक्य बालिका रोदितुमारब्धा। तं निवारयन्ती सा प्रार्थयत्- “तण्डुलान् मा भक्षया मदीया माता अतीव निर्धना वर्तते।” स्वर्णपक्षः काकः प्रोवाच, “मा शुचः। सूर्योदयात्प्राग् ग्रामाद्बहिः पिप्पलवृक्षमनु त्वया आगन्तव्यम्। अहं तुभ्यं तण्डुलमूल्यं दास्यामि।” प्रहर्षिता बालिका निद्रामपि न लेभे।

शब्दार्थाः – पुरा = प्राचीनकाले (प्राचीन समय में), कस्मिंश्चिद् = कस्मिन् चित् (किसी), ग्रामे = वसथे (गाँव में), एका निर्धना = एका दरिद्रा (एक गरीब), स्त्री = वनिता (महिला/स्त्री), न्यवसत् = वसति स्म (रहती थी), तस्याः = (उसकी), एका दुहिता = एका पुत्री (एक पुत्री), विनम्रा = विनयशीला (विनम्र), मनोहरा = हृदयहारिणी (मनोहर), च = और, आसीत् = अवर्तत (थी), एकदा = एकस्मिन् दिवसे (एक बार), माता = जननी (माता ने), स्थाल्याम् = स्थालीपात्रे (थाली में), तण्डुलान् = अक्षतान् (चावलों को), निक्षिप्य = प्रसार्य (फैलाकर/रखकर), पुत्रीम आदिशत् = आदेशमददत् (आदेश दिया), सूर्यातपे = आतपे (धूप में),

तण्डुलान् = अक्षतान् (चावलों को), खगेभ्यः = विहगेभ्यः (पक्षियों से), रक्ष = रक्षणं कुरु (रक्षा करो), किञ्चित् कालादनन्तरम् = ईषत् समयपश्चात् (कुछ समय के पश्चात्), एको विचित्रः काकः = एकः विचित्र: वायसः (एक अजीब कौआ), समुड्डीय = उत्प्लुत्य (उड़कर), तस्याः समीपम् अगच्छत् = ताम् समीपम् आगतवान् (उसके पास पहुँचा), न = मा (नहीं), एतादृशः = एतस्य प्रकारस्य (इस प्रकार का), स्वर्णपक्षः = स्वर्णमये पक्षे यस्य सः (सोने के पंखों वाला), रजतचञ्चुः = रजतमय: चञ्चुः यस्य सः (चाँदी की चोंच वाला), स्वर्णकाकः = स्वर्णस्य वायसः (सोने का कौआ/सुनहला कौआ), तया = (उस (लड़की) के द्वारा),

पूर्वम् = पुरा (पहले), दृष्टः = अपश्यत् (देखा था), तम् = उस (कौए) को), तण्डुलान् = अक्षतान् (चावलों को), खादन्तम् = भक्षयन्तम् (खाते हुए), हसन्तम् = हास्यं कुर्वन्तम् (हँसते हुए), च = और, विलोक्य = दृष्ट्वा (देखकर), बालिका = कन्या (उस लड़की ने), रोदितुम् = विलपितुम् (रोना), आरब्धा = प्रारम्भम् अकरोत् (शुरू कर दिया), तम् = (उस कौए को), निवारयन्ती = वारणं कुर्वन्ती (रोकती हुई), सा = (वह), प्रार्थयत् = न्यवेदयत् (प्रार्थना करने लगी), तण्डुलान् = अक्षतान् (चावलों को), मा = न (नहीं/मत), भक्षय = खाद (खाओ), मदीया = मम (मेरी), माता = जननी (माता), अतीव = अत्यन्तम् (अत्यन्त/अत्यधिक),

निधन = वित्तहीना/दरिद्रा (गरीब), वर्तते = अस्ति (है), स्वर्णपक्षः काकः = स्वर्णमये पक्षे यस्य सः (सोने के पंखों वाला/सुनहला कौआ), प्रोवाच = अकथयत् (कहा), मा शुचः = शोक मा कुरु (शोक मत करो), सूर्योदयात्प्राग् = भानूदयात् पूर्वम् (सूर्योदय से पहले), ग्रामाबहिः = गाँव के बाहर, पिप्पलवृक्षमनु = पिप्पलतरो: अधः (पीपल के पेड़ के नीचे), त्वया = भवत्या (तुम्हारे द्वारा), आगन्तव्यम् = आगच्छेत् (आना चाहिए), अहम् = मैं, तुभ्यम् = ते/भवत्यै (तुम्हारे लिए), तण्डुलमूल्यम् = अक्षतमूल्यम् (चावलों का मूल्य), दास्यामि = अर्पणं करिष्यामि (दूँगा), प्रहर्षिता = प्रसन्ना (खुश हुई), बालिका = कन्या (लड़की ने), निद्रामपि न लेभे = शयनम् अपि न प्राप्तम् अकरोत् (नींद भी नहीं ली/सोई भी नहीं)।

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश श्रीपद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नामक कथा-संग्रह से उद्धृत ‘स्वर्णकाक:’. नामक पाठ से अवतरित है।

प्रसंग – प्रस्तुत गद्यांश में धूप में रखे बालिका द्वारा रक्षित चावलों को सुनहले कौए द्वारा खाने और चावलों का मूल्य चुकाने के लिए कहने का वर्णन है।

हिन्दी-अनुवाद – प्राचीन समय में किसी गाँव में एक गरीब वृद्ध महिला रहती थी। उसकी एक विनम्र और मनोहर पुत्री थी। एक बार माता ने थाली में चावलों को रखकर पुत्री को आदेश दिया-धूप में रखे चावलों की पक्षियों से रक्षा करना। कुछ समय पश्चात् एक अजीब कौआ उड़कर उसके पास पहुँचा।

इस प्रकार का सोने के पंखों वाला, चाँदी की चोंच वाला सुनहला कौआ उसने पहले नहीं देखा था। उसको चावलों को खाता हुआ और हँसता हुआ देखकर लड़की ने रोना शुरू कर दिया। उसको रोकते हुए वह प्रार्थना करने लगी-चावलों को मत खाओ। मेरी माता बहुत गरीब है। सुनहला कौआ बोला-दुखी मत होओ। तुम सूर्योदय से पहले गाँव के बाहर पीपल के पेड़ के नीचे आना। मैं तुम्हें चावलों का मूल्य दूंगा। खुश (प्रसन्न) हुई लड़की को नींद भी नहीं आई अर्थात् वह सोई भी नहीं।

संस्कत-व्याख्याः

सन्दर्भ: – प्रस्तुतगद्यांशः अस्माकं पाठ्यपुस्तकात् शेमुष्याः ‘स्वर्णकाकः’ नामक पाठात् अवतरितोऽस्ति। प्रस्तुतपाठः श्री पद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम्’ नामक कथासंग्रहात् सङ्कलितः अस्ति। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक. ‘शेमुषी’ के ‘स्वर्णकाकः’ नामक पाठ से लिया गया है। प्रस्तुत पाठ श्री पद्म शास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नाम के कथा ग्रन्थ से संकलित है।)

प्रसङ्गः – प्रस्तुतगद्यांशे वर्णितं यदेक: स्वर्णकाकः सूर्यातपे स्थाल्यां स्थितान् बालिकया रक्षितान् अक्षतान् खादति तेषां मूल्यं च प्रदातुं कथयति। (प्रस्तुत गद्यांश में वर्णित है कि एक सोने का कौआ धूप में थाली में रखे चावलों को खाता है और उनका मूल्य चुकाने के लिए कहता है।)

व्याख्याः – प्राचीनकाले कस्मिन् अपि वसथे (ग्रामे) एका दरिद्रा वृद्धा वनिता (स्त्री) वसति स्म। तस्याः एका विनयशीला हृदयहारिणी च पुत्री आसीत्। एकस्मिन् दिवसे जननी स्थाल्यां अक्षतान् प्रसार्य सुतायै आदेशम् अददात् यत् सूर्यातपे अक्षतानां विहगेभ्यः रक्षणं कुरु। ईषत् समयपश्चात् एकः विचित्रवायसः उत्प्लुत्य तस्याः समीपम् आगच्छत् । न तस्य प्रकारस्य हेममयः पक्षः रजतमयः चञ्चुः स्वर्णकाकः एतया पुरा दृष्टः। तम् (स्वर्णकाकम्) अक्षतान् भक्षयन्तम् हास्यं च कुर्वन्तं दृष्ट्वा सा कन्या विलपितुम् आरभत।

काकं वारयन्ती सा न्यवेदयत्- अक्षतान् मा खाद। मम जननी अत्यन्त दरिद्रा अस्ति। हेममयः पक्षः वायसः अकथयत्-शोकं मा कुरु। भानूदयात् पूर्वं ग्रामात् बहिः पिप्पलतरा: अधः भवती आगच्छे। अहं भवत्यै अक्षतमूल्यम् अर्पणं करिष्यामि। प्रसन्ना कन्या शयनम् अपि न प्राप्तम् अकरोत्। (प्राचीनकाल में किरा में एक गरीब बुढ़िया रहती थी। उसकी एक विनम्र, हृदय को हरण करने वाली बेटी थी। एक दिन माता ने थाली में चावलों को फैलाकर पुत्री को आदेश दिया कि सूर्य की धूप तक चावलों की पक्षियों से रक्षा करो।

कुछ समय बाद एक विचित्र कौआ उड़कर उसके पास आया। इस प्रकार का सोने के पंखों वाला और चाँदी की चोंच वाला कौआ इससे पहले नहीं देखा गया। उस (सोने के कौवे) को चावल चुगते हुए और हँसते हुए को देखकर वह कन्या रोने लगी। कौए को रोकती हुई उसने निवेदन किया-“चावलों को मत खाओ। मेरी माता बहुत गरीब है।” सोने की चोंच वाले कौवे ने कहा-“दुखी मत हो। सूरज निकलने से पहले गाँव के बाहर पीपल के नीचे आप आ जाना। मैं आपके लिए चावलों का मूल्य सौंप दूंगा।” खुश हुई कन्या सो भी नहीं पाई।)

अवबोधन कार्यम्

प्रश्न 1.
एकपदेन उत्तरत- (एक शब्द में उत्तर दीजिए-)
(क) बालिका तण्डुलान् केभ्यः रक्षेतु? (बालिका किनसे चावलों की रक्षा करे?)
(ख) ‘तण्डुलान् मा खादय’ इति कोऽवदत्? (‘चावल मत खाओ’ ऐसा किसने कहा?)

प्रश्न 2.
पूर्णवाक्येन उत्तरत – (पूरे वाक्य में उत्तर दीजिए-)
(क) बालिका केन कारणेन रोदितुम् आरब्धा? (बालिका किस कारण से रोई ?)
(ख) कीदृशः काकः बालिकया पूर्वं न दृष्टः? (बालिका ने कैसा कौआ पहले नहीं देखा?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) “स्वर्णपक्षी’ इत्यत्र किं पदं विशेषण पदम् ?। (‘स्वर्णपक्षी’ इनमें कौनसा पद विशेषण पद है?)
(ख) ‘धनविहीना’ इति पदस्य समानार्थी गद्यांशात् चित्वा लिखत।
(‘धनविहीना’ इस पद का समानार्थी पद गद्यांश से लिखिए।)
उत्तराणि :
(1) (क) खगेभ्यः। (पक्षियों से)।
(ख) बालिका (लड़की ने)।

(2) (क) तण्डुलान् खादन्तं हसन्तं तं काकम् अवलोक्य बालिका रोदितुम् आरब्धा। (चावलों को खाते हुए हँसते हुए उस कौआ को देखकर लड़की रोने लगी।)
(ख) नैतादृशः स्वर्णपक्षो रजतचञ्चुः स्वर्ण काकस्तया पूर्व दृष्टः। (ऐसा सोने की पंखों और चाँदी की चोंच वाला सोने का कौए उसने पहले नहीं देखा था।)

(3) (क) स्वर्ण (सोना)।
(ख) निर्धना (गरीब)।

2. सूर्योदयात्पूर्वमेव सा तत्रोपस्थिता। वृक्षस्योपरि विलोक्य सा च आश्चर्यचकिता सञ्जाता यत् तत्र स्वर्णमयः प्रासादो वर्तते। यदा काकः शयित्वा प्रबुद्धस्तदा तेन स्वर्णगवाक्षात्कथितं “हहो बाले! त्वमागता, तिष्ठ, अहं त्वत्कृते सोपानमवतारयामि, तत्कथय स्वर्णमयं रजतमयम् ताम्रमयं वा”? कन्या अवदत् “अहं निर्धनमातुः दुहिता अस्मि। ताम्रसोपानेनैव आगमिष्यामि।” परं स्वर्णसोपानेन सा स्वर्ण-भवनम् आरोहता।

शब्दार्थाः – सूर्योदयात्यूर्वमेव = भानूदयात् प्राग् एव (सूर्योदय से पहले ही), सा = (वह (बालिका)), तत्रोपस्थिता = तस्मिन् स्थाने सन्निहिता (वहाँ उपस्थित हो गयी), वृक्षस्योपरि = तरोः उपरि (पेड़ के ऊपर), विलोक्य = दृष्ट्वा (देखकर), सा = (वह), च = (और), आश्चर्यचकिता = विस्मिता (आश्चर्यचकित), सञ्जाता = अभवत् (हो गयी), यत् = (कि), तत्र = तस्मिन् स्थाने (उस जगह/वहाँ) स्वर्णमयः = हेममयः (सोने का), प्रासादः = राजमन्दिरम् (महल), वर्तते = अस्ति (है), यदा = यस्मिन् समये (जब),

काकः = वायसः (कौआ), शयित्वा = शयनं कृत्वा (सोकर), प्रबुद्धः = जागरणम् अकरोत् (जागा), तदा = तस्मिन् समये (तब), तेन = काकेन (उस कौए ने), स्वर्णगवाक्षात् = हेममयवातायनात् (सोने की खिड़की से), कथितं = अकथयत् (कहा), हं हो बाले! = भो बाले (अरे बालिका), त्वमागता = भवती आगता (तुम आ गई हो), तिष्ठ = स्थिरा भव (ठहरो), अहम् = मैं, त्वत्कृते = तुभ्यम् (तुम्हारे लिए), सोपानम् = (सीढ़ी), अवतारयामि = अवतीर्णं करोमि (उतारता हूँ), तत्कथय = तु वद (तो बोलो),

स्वर्णमयं = हेममयं (सोने से बनी, सोने की), रजतमयं = रूप्यमयं (चाँदी से बनी, चाँदी की), वा = (अथवा), ताम्रमयं = लोहितायसमयं (ताँबे से बनी, ताँबे की), कन्या = बालिका (लड़की), अवदत् = प्रावोचत् (बोली), अहं निर्धनमातुः = अहं दरिद्रायाः जनन्याः (मैं निर्धन/गरीब माँ, ताम्रसोपानेनैव = लोहितायसेन निर्मितेन सोपानेन एव (ताँबे की बनी सीढ़ी से ही), आगमिष्यामि = आगमनं करिष्यामि (आऊँगी), परं = परञ्च (लेकिन), स्वर्णसोपानेन = हेमनिर्मितसोपानेन (सोने की सीढ़ी से), स्वर्णभवनम् = हेममयं भवनम् (सोने के महल को), सा = (वह), आरोहत = आरूढवती

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश श्री पद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नामक कथा-संग्रह से उद्धृत ‘स्वर्णकाकः’ नामक पाठ से अवतरित है।

प्रसंग – प्रस्तुत गद्यांश में बालिका के सूर्योदय से पहले ही गाँव के बाहर पीपल के पेड़ के नीचे पहुँचकर पेड़ के ऊपर सोने के महल को देखकर आश्चर्यचकित होने एवं सोने की सीढ़ियों से स्वर्णमहल में पहुँचने का वर्णन है।

हिन्दी-अनुवाद – सूर्योदय से पहले ही वह (लड़की) वहाँ आ गयी। पेड़ के ऊपर देखकर वह आश्चर्यचकित हो गयी क्योंकि वहाँ सोने का महल था। जब कौआ सोकर जागा तब उसने सोने की खिड़की में से (झाँककर) कहा-अरे लड़की! तुम आ गयी हो, ठहरो, मैं तुम्हारे लिए सीढ़ी उतारता हूँ, तो कहो सोने से बनी (सोने की), चाँदी से बनी (चाँदी की) अथवा ताँबे से बनी (ताँबे की)? लड़की बोली-मैं गरीब माता की बेटी हूँ। ताँबे की बनी सीढ़ी से ही आऊँगी। लेकिन सोने की सीढ़ी से वह सोने के महल में पहुँची।

संस्कत-व्याख्याः

सन्दर्भः – प्रस्तुतगद्यांश अस्माकं पाठ्यपुस्तकात् शेमुष्याः ‘स्वर्णकाकः’ पाठात् उद्धृतः। पाठोऽयं श्री पद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम्’ इति कथासंग्रहात् संकलितो वर्तते। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक शेमुषी से ‘स्वर्णकाकः’ पाठ से उद्धृत है। यह पाठ श्री पद्म शास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ कथा-संग्रह से सङ्कलित है।)

प्रसङ्गः – गद्यांशोऽयम् वर्णयति यत् बालिका काकेन निर्दिष्टस्थानम् अगच्छत्, तत्र च गत्वा सा वृक्षस्योपरि स्वर्णमयप्रासादं दृष्ट्वा विस्मिता जाता। (यह गद्यांश वर्णन करता है कि लड़की कौवा द्वारा बताये गये स्थान पर गई और वहाँ जाकर वह वृक्ष के ऊपर सोने के महल को देखकर आश्चर्यचकित हो गई।)

व्याख्याः – सा बालिका भानूदयात् प्राग् एव काकेन निर्दिष्ट स्थानं आगच्छत् । वृक्षस्य उपरि दृष्ट्वा सा विस्मिता अभवत् यत् तत्र हेममयं प्रासादम् आसीत्। यदा काकः शयनं कृत्वा जागरणम् अकरोत् तदा स हेममयात् वातायनात् अकथयत्-हे बाले! त्वम् आगतवती, स्थिरा भव अहं तुभ्यं सोपानम् अवतीर्णं करोमि, कथय तु हेममयं सोपानं रजतमयं ताम्रमयं वा? बालिका अवदत् यदहं दरिद्रायाः जनन्याः पुत्री अस्मि, ताम्रमयेन एव सोपानेन आगमिष्यामि। परञ्च सा हेममयेन सोपानेन हेममयं प्रासादं प्राप्तम् अकरोत्। (वह लड़की सूरज उगने से पहले ही कौआ द्वारा बताये हुए स्थान पर पहुँच गई।

पेड़ के ऊपर देखकर वह आश्चर्यचकित हो गई कि वहाँ सोने का महल था। जब कौआ सोकर जागा तब उसने सोने की खिड़की से कहा-‘हे बालिका तुम आ गई, ठहरो, मैं तुम्हारे लिए सीढ़ी उतारता हूँ, कहो तो सोने की, चाँदी की या ताँबे की?” लड़की बोली कि “मैं गरीब माँ की बेटी हूँ, ताँबे की सीढ़ी से ही आ जाऊँगी। परन्तु वह सोने की सीढ़ी से ही सोने के महल पर पहुँची।)

अवबोधन कार्यम्

प्रश्न 1.
एकपदेन उत्तरत – (एक शब्द में उत्तर दीजिए-)
(क) बालिका तत्र कदा उपस्थिता? (बालिका कहाँ कब उपस्थित हो गई?)
(ख) काकस्य प्रासादः कुत्र आसीत् ? (कौवे का महल कहाँ था?)

प्रश्न 2.
पूर्णवाक्येन उत्तरत – (पूरे वाक्य में उत्तर दीजिए-)
(क) बालिका कस्मात् आश्चर्यचकिता सञ्जाता? (बालिका किसलिए आश्चर्यचकित हो गई?)
(ख) कन्या काकं किम् अवदत्? (कन्या ने कौवे से क्या कहा?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) ‘विलोक्य’ इति पदे प्रत्ययं लिखत। (‘विलोक्य’ पद में प्रत्यय लिखिए।)
(ख) ‘स्वर्णमयः प्रासादः वर्तते’ एतेषु वाक्येषु विशेषणं विशेष्यं च पदम् निर्दिशत।
(यहाँ विशेषण और विशेष्य पदों का निर्देश कीजिए।)
उत्तराणि :
(1) (क) सूर्योदयात्पूर्वम् (सूर्य निकलने से पहले)।
(ख) वृक्षस्योपरि। (वृक्ष के ऊपर)।

(2) (क) वृक्षस्योपरि स्वर्णमयं प्रासादम् अवलोक्य आश्चर्यचकिता सञ्जाता। (वृक्ष के ऊपर सोने के महल को
देखकर आश्चर्यचकित हो गई।)
(ख) अहं निर्धनमातुः दुहिता अस्मि ताम्र सोपानेनैव आगमिष्यामि। (मैं गरीब माँ की बेटी हूँ। ताँबे की सीढ़ी से ही आ जाऊँगी।)

(3) (क) ल्यप्।
(ख) विशेषणम्-स्वर्णमयः, विशेष्यं च-प्रासादः।

3. चिरकालं भवने चित्रविचित्रवस्तूनि सज्जितानि दृष्ट्वा सा विस्मयं गता। श्रान्तां तां विलोक्य काकः अवदत्-“पूर्वं लघुप्रातराशः क्रियताम्-वद त्वं स्वर्णस्थाल्यां भोजनं करिष्यसि किं वा रजतस्थाल्याम् उत ताम्रस्थाल्याम्”? बालिका अवदत्- ताम्रस्थाल्याम् एव अहं – “निर्धना भोजनं करिष्यामि।” तदा सा आश्चर्यचकिता सञ्जाता यदा स्वर्णकाकेन स्वर्णस्थाल्यां भोजनं “परिवेषितम्।” न एतादृशम् स्वादु भोजनमद्यावधि बालिका खादितवती। काकोऽवदत्- बालिके! अहमिच्छामि यत् त्वम् सर्वदा अत्रैव तिष्ठ परं तव माता तु एकाकिनी वर्तते। अत: “त्वं शीघ्रमेव स्वगृहं गच्छ।”

शब्दार्थाः – चिरकालम् = बहुकालं यावत् (बहुत देर तक), भवने = प्रासादे (महल में), चित्रविचित्रवस्तूनि = अद्भुतानि वस्तूनि (अद्भुत वस्तुओं को), सज्जितानि = अलंकृतानि (सजी हुई), दृष्ट्वा = विलोक्य (देखकर), सा = (वह), विस्मितम् = आश्चर्यचकितम् (आश्चर्यचकित), गता = सञ्जाता (हुई), श्रान्ताम् = क्लान्तां (थकी हुई), ताम् = (उसे), विलोक्य = दृष्ट्वा (देखकर), काकः = वायसः (कौआ),

अवदत् = प्राह (बोला), पूर्वम् = प्राग् (पहले), लघुप्रातराशः = लघुकल्यवर्तः (थोड़ा सुबह का नाश्ता), क्रियताम् = करोतु (करो), वद = कथय (बोलो), त्वम् = (तुम), स्वर्णस्थाल्याम् = स्वर्णेन निर्मितस्थाल्यां (सोने की थाली में), भोजनम् = अशनम् (भोजन), करिष्यसि = (करोगी), किं वा = अथवा (अथवा), रजतस्थाल्याम् = रूप्येन निर्मितस्थाल्यां (चाँदी की थाली में), अकथयत् = व्याजहार (कहा), ताम्रस्थाल्याम् = लोहितायसेन निर्मितस्थाल्यां (ताँबे की थाली में), एव = निश्चयेन (ही), अहम् = मैं, निर्धना = दरिद्रा (निर्धन), भोजनम् = अशनम् (भोजन), करिष्यामि = (करूँगी), तदा = तस्मिन् समये (तब), सा = वह (लड़की), आश्चर्यचकिता = विस्मिता (आश्चर्यचकित),

सजाता = गता (हो गई), यदा = यस्मिन् काले (जब), स्वर्णकाकेन = हेमवायसेन (सुनहले कौए ने), स्वर्णस्थाल्याम् = स्वर्णेन निर्मितस्थाल्यां (सोने की थाली में), भोजनम् = अशनम् (भोजन), परिवेषितम् = पर्यवेषणं कृतम् (परोसा), न = मा (नहीं), एतादृशम् = ईदृशं (ऐसा), स्वादु = स्वादिष्टम् (स्वादिष्ट), भोजनम् = अशनं (भोजन), अद्यावधि = वर्तमानं दिनं यावत् (आज तक), बालिका = सा कन्या (उस लड़की ने), खादितवती = भक्षितवती (खाया था),

काकः = वायसः (कौआ), अवदत् = ब्रूते (बोला), बालिके = कन्ये (बालिका), अहमिच्छामि = अहमभिलषामि (मैं चाहता हूँ), यता = कि, त्वम् = (तुम), सर्वदा = सर्वस्मिन् काले (हमेशा), अत्रैव = एतस्मिन् स्थाने एव (यहीं), तिष्ठ = वासं कुरु (रहो), परम् = परञ्च (लेकिन), तव = ते (तुम्हारी), माता = जननी (माता), वर्तते = अस्ति (है), एकाकिनी = एकला (अकेली), वम् = (तुम), शीघ्रमेव = द्रुतमेव (शीघ्र ही), स्वगृहम् = स्वगेहं (अपने घर), गच्छ = गमनं कुरु (जाओ)।

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ के ‘स्वर्णकाकः’ नामक पाठ से उद्धृत है। यह पाठ श्री . । . पद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नामक कथा-संग्रह से संकलित है।।

प्रसंग – यहाँ वर्णन है कि सोने के महल में सुनहले कौए ने बालिका के साथ कैसा व्यवहार किया।

हिन्दी-अनुवाद – बहुत देर तक महल में अत्यन्त अदभुत वस्तुओं को सजी हुई देखकर वह आश्चर्यचकित हो गयी। उसे थकी हुई देखकर कौआ उससे बोला कि पहले आप थोड़ा-सा सुबह का नाश्ता कर लो, बोलो तो सोने की थाली में भोजन करोगी अथवा चाँदी की थाली में या ताँबे की थाली में ? लड़की बोली कि मैं गरीब हूँ, मैं तो ताँबे की थाली में ही भोजन करूँगी। तब वह आश्चर्यचकित हो गयी जब सुनहले कौए ने उसे सोने की थाली में भोजन परोसा। लड़की ने ऐसा स्वादिष्ट भोजन आज तक नहीं खाया था। कौआ उससे बोला कि मैं चाहता हूँ कि तुम हमेशा यहीं रहो लेकिन तुम्हारी माता अकेली हैं। अतः तुम जल्दी ही अपने घर जाओ।

संस्कत-व्याख्याः

सन्दर्भ: – प्रस्तुतः गद्यांशः अस्माकं पाठ्यपुस्तकात् शेमुष्याः ‘स्वर्णकाकः’ पाठात् उद्धृतः। पाठोऽयं श्रीपद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम्’ इति कथासंग्रहात् सङ्कलितो वर्तते। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ के स्वर्णकाकः’ पाठ से उद्धृत है। यह पाठ श्रीपद्मशास्त्री-रचित ‘विश्वकथाशतकम्’ से संकलित है।)

प्रसंग: – वर्णितमत्र यत् स्वर्णकाक: स्वप्रासादे बालिकया सह कीदृशं व्यवहारम् अकरोत्। (इसमें बालिका के साथ कौआ के सद्व्यवहार का वर्णन किया गया है।)

व्याख्या: – बहकालं यावत् स्वर्णप्रासादे अलङ्कृतानि अति अद्भुतवस्तुनि विलोक्य सा आश्चर्यचकिता अभवत्। तां क्लान्तां दृष्ट्वा काकः तामवदत् यत् पूर्वं भवती लघुकल्यवर्तं करोतु, कथय तु स्वर्णमयस्थाल्यां, रजतमयस्थाल्यां ताम्रमयस्थाल्यां वा भोजनं करिष्यसि। बालिका अवदत् यदहं निर्धना अस्मि, अहं तु ताम्रमयस्थाल्यामेव अशनं करिष्यामि। यदा स्वर्णकाकः तस्यै स्वर्णमयस्थाल्यां भोजनम् अददात्। तदा सा चकिता अभवत्। बालिका ईदृशं स्वादिष्टभोजनं वर्तमानं दिनं यावत् न अखादत्। काकः तामवदत् यदहम् अभिलषामि यत् त्वम् सदा अत्रैव वासं कुरु परं तव माता एकला अस्ति। अतः त्वं शीघ्रम् एव स्वगृहं गच्छ।

(बहुत देर तक सोने के महल में सजी हुई अनोखी वस्तुओं को देखकर वह आश्चर्यचकित हो गई। उसे थका हुआ देखकर उससे कौआ बोला कि पहले आप थोड़ा कलेवा कर लो, बोलो तुम सोने की थाली में, चाँदी की थाली में या ताँबे की थाली में भोजन करोगी। बालिका बोली कि मैं गरीब हूँ, मैं तो ताँबे की थाली में ही खाना खाऊँगी (भोजन करूँगी)। जब सोने का कौवा उसके लिए सोने की थाली में भोजन लाया तो वह चकित हो गई। लड़की ने ऐसा स्वादिष्ट भोजन आज तक नहीं खाया। कौआ उससे बोला कि मैं चाहता हूँ कि तुम सदा यहाँ ही रहो परन्तु तुम्हारी माता अकेली हैं। अतः तुम शीघ्र ही अपने घर चली जाओ।)

अवबोधन कार्यम्

प्रश्न 1.
एकपदेन उत्तरत- (एक शब्द में उत्तर दीजिए-)
(क) कानि दृष्ट्वा बालिका विस्मयं गता? (किन्हें देखकर बालिका आश्चर्य करने लगी?) ।
(ख) स्वर्णकाकेन तस्मै कस्यां भोजनं पर्यवेषितम् ? (सोने के कौवे ने कैसी थाली में उसे भोजन परोसा?)

प्रश्न 2.
पूर्णवाक्येन उत्तरत- (पूरे वाक्य में उत्तर दीजिए-)
(क) काक: बालिका कस्मात् न वारयति स्म? (कौवे ने बालिका को क्यों नहीं रोका?)
(ख) श्रान्तां बालिकाम् अवलोक्य काकः किं कर्तुम् अवदत् ? (थकी बालिका को देखकर कौवे ने क्या करने के लिए कहा?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) ‘दृष्ट्वा सा विस्मयं गता’ अत्र सा इति सर्वनाम पदं कस्मै प्रयुक्तम्? (‘दृष्ट्वा सा विस्मयं गता’ यहाँ ‘सा’ सर्वनाम पद किसके लिए प्रयोग हुआ है?)
(ख) ‘त्वं शीघ्रमेव स्वगृहं गच्छ’ इति कः कम् अकथयत् ? (‘तुम शीघ्र अपने घर जाओ’ यह किसने किससे
कहा?)
उत्तराणि :
(1) (क) चित्रविचित्र वस्तूनि (रंग-बिरंगी अद्भुत वस्तुओं को)।
(ख) स्वर्णस्थाल्याम् (सोने की थाली में)।

(2) (क) यतः तस्य माता गृहे एकाकिनी अस्ति। (क्योंकि उसकी माँ घर पर अकेली है।) श्रान्तां बालिका अवलोक्य काकः लघुप्रातराशं कर्तुम् अवदत्। (थकी बालिका को देखकर कौवे ने थोड़ा कलेवा करने के लिए कहा।)

(3) (क) बालिकायै (बालिका के लिए।)
(ख) काकः बालिकाम् अकथयत्। (कौवे ने बालिका से कहा।)

4. इत्युक्त्वा काकः कक्षाभ्यन्तरात् तिम्रः मञ्जूषाः निस्सार्य तां प्रत्यवदत्- “बालिके! यथेच्छं गृहाण मञ्जूषामेकाम्।” लघुतमा मञ्जूषां प्रगृह्य बालिकया कथितम् इयत् एत्र मदीयतण्डुलानां मूल्यम्।
गृहमागत्य तया मञ्जूषा समुद्घाटिता, तस्यां महार्हाणि हीरकाणि विलोक्य सा प्रहर्षिता तद्दिनाद्धनिका च सजाता।

शब्दार्थाः – इत्युक्त्वा = एवं कथयित्वा (ऐसा कहकर), काकः = वायसः (कौए ने), कक्षाभ्यन्तरात् = कोष्ठस्य गर्भात् (कमरे के अन्दर से), तिस्त्रः = तीन, मञ्जूषाः = पेटिकाः (पेटियाँ), निस्सार्य = निष्कासनं कृत्वा (निकालकर), ताम् = उससे, लड़की से, प्रत्यवदत् = अकथयत् (कहा), बालिके = कन्ये (बाला), यथेच्छम् = इच्छानुसारेण (अपनी इच्छा के अनुसार), गृहाण = ग्रहणं कुरु (ले लो), मञ्जूषामेकाम् = एकां पेटिकां (एक पेटी), लघुतमाम् = क्षुद्रतमा (सबसे स्वकाकः छोटी), मञ्जूषाम् = पेटिकां (पेटी को),

प्रगृह्य = ग्रहणं कृत्वा (लेकर), बालिकया = कन्यया (बालिका द्वारा), कथितम् = उक्तम् (कहा गया), इयत् एव = एतन्मात्रम् एव (इतना ही), मदीय = मम (मेरे), तण्डुलानाम् = अक्षतानां (चावलों का), मूल्यम् = अर्घम् (कीमत/मूल्य), गृहमागत्य = सदनमागत्य (घर आकर), तया = (उसके द्वारा), मञ्जूषा = पेटिका (पेटी), समुद्घाटिता = भेदनं कृतं (खोली गई), तस्याम् = (उसमें), महार्हाणि = बहुमूल्यानि (बहुमूल्य), हीरकाणि – रत्नमुख्यानि (हीरों को), विलोक्य = दृष्ट्वा (देखकर), सा = (वह), प्रहर्षिता = आनन्दिता अभवत् (आनन्दित हुई), तदिनाद्धनिका = तस्मात् वासरात् धनिका (उसी दिन से धनवती), सजाता = अभवत् (हो गई)।

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश हमारी पाठ्य-पुस्तक ‘शेमुषी’ के ‘स्वर्णकाकः’ नामक पाठ से उद्धृत है। यह पाठ श्री। पद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नामक कथा-संग्रह से संकलित है।

प्रसंग – यहाँ लड़की के लोभरहित होने तथा कौए की उसके प्रति उदारता का वर्णन है।

हिन्दी-अनुवाद – ऐसा कहकर कौए ने कमरे के अन्दर से तीन पेटियाँ (सन्दूकें) निकालकर उससे कहा-बालिका! अपनी इच्छानुसार एक सन्दूक ले लो। सबसे छोटी सन्दूक लेकर लड़की ने कहा-यह ही मेरे चावलों का मूल्य है। घर आकर उसने सन्दूक खोला, उसमें (सन्दूक में) बहुमूल्य हीरों को देखकर वह प्रसन्न हो गयी और उसी दिन से धनिक हो गई।

संस्कत-व्यारव्याः

सन्दर्भ: – प्रस्तुतगद्यांशः अस्माकं पाठ्यपुस्तकात् शेमुष्या: ‘स्वर्णकाकः’ पाठात् उद्धृतः। पाठोऽयं श्रीपद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम् इति कथासंग्रहात् संकलितो वर्तते। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ से ‘स्वर्णकाकः’ पाठ से लिया गया है। यह पाठ श्री पद्मशास्त्री-रचित ‘विश्वकथाशतकम्’ कथा-संग्रह से संकलित है।)

प्रसंग: – गद्यांशोऽयं वर्णयति बालिकायाः लोभराहित्यं काकस्य च तां प्रति औदार्यम्। (यह गद्यांश बालिका की । लोभहीनता तथा कौए की उसके प्रति उदारता का वर्णन करता है।)

व्याख्या: – एवं कथयित्वा काकः कोष्ठस्य गर्भात् तिस्रः पेटिकाः बहिः आनीय तां (बालिकाम्) अवदत्-हे बालिके! स्वेच्छया एकां पेटिकां गृहाण। बालिका क्षुद्रतमां पेटिकां गृहीत्वा अवदत्-एतन्मात्रम् मम अक्षतानां अर्घम् अस्ति। गृहम् आगत्य सा पेटिकाम् उद्घाटयत्। तस्यां बहुमूल्यानि हीरकाणि दृष्ट्वा सा प्रसन्ना अभवत्। तस्मात् वासरात् च धनवती अभवत्। (इस प्रकार कहकर कौआ ने कोटर से तीन पेटियाँ लाकर उस बालिका से कहा-हे बालिके! अपनी इच्छा से एक पेटी ले लो। बालिका ने सबसे छोटी पेटी को लेकर कहा-‘इतना ही मेरे चावलों का मूल्य है।’ घर आकर उसने पेटी को खोला। उसमें बहुमूल्य हीरों को देखकर वह प्रसन्न हो गई। उसी दिन से वह धनवाली (धनाढ्य) हो गई।)

अवबोधन कार्यम्

प्रश्न 1.
एकपदेन उत्तरत- (एक शब्द में उत्तर दीजिए-)
(क) काकः कति मञ्जूषाः आनयत? (कौवा कितनी पेटियाँ लाया?)
(ख) बालिका कीदृशी मञ्जूषां गृहीतवती? (बालिका ने कैसी पेटी ली?)

प्रश्न 2.
पूर्णवाक्येन उत्तरत- (पूरे वाक्य में उत्तर दीजिए-)
(क) मञ्जूषायां कानि आसीत्? (कितनी मंजूषाएँ थीं ?)
(ख) मञ्जूषां प्रगृह्य बालिका किमवदत् ? (पेटी को पाकर लड़की ने क्या कहा?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) ‘तां प्रत्यवदत्’ अत्र ‘ताम्’ इति सर्वनाम पदं कस्य स्थाने प्रयुक्तम्? (तां प्रत्यवदत् यहाँ ‘ताम्’ सर्वनाम किसके लिए प्रयोग हुआ है?)
(ख) गद्यांशात् ‘पेटिका’ इति पदस्य पर्यायं चित्वा लिखत। (गद्यांश से ‘पेटिका’ का पर्यायवाची लिखिए।)
उत्तराणि :
(1) (क) तिस्रः (तीन)।
(ख) लघुतमाम् (सबसे छोटी को)।

(2) (क) मञ्जूषायां बहुमूल्यानि हीरकाणि आसन्। (मंजूषा में महँगे हीरे थे।)
(ख) तया कथतम् इयम् मे तण्डुलानां मूल्यम्। (यह मेरे चावलों की कीमत है, ऐसा उसने कहा।)

(3) (क) बालिकाम् (बालिका को)।
(ख) मञ्जूषा (पेटी)।

5. तस्मिन्नेव ग्रामे एका अपरा लुब्धा वृद्धा न्यवसत्। तस्या अपि एका पुत्री आसीत्। ईर्ष्णया सा तस्य स्वर्णकाकस्य रहस्यम् ज्ञातवती। सूर्यातपे तण्डुलान् निक्षिप्य तयापि स्वसुता रक्षार्थं नियुक्ता। तथैव स्वर्णपक्षः काकः तण्डुलान् भक्षयन् तामपि तत्रैवाकारयत्। प्रातस्तत्र गत्वा सा काकं निर्भयन्ती प्रावोचत्-“भो नीचकाक! अहमागता, मां तण्डुलमूल्यं प्रयच्छ।” काकोऽब्रवीत्-“अहं त्वत्कृते सोपानम् अवतारयामि। तत्कथय स्वर्णमयं रजतमयं ताम्रमयं वा।” गर्वितया बालिकया प्रोक्तम्-“स्वर्णमयेन सोपानेन अहम् आगच्छामि।” परं स्वर्णकाकस्तत्कृते ताम्रमयं सोपानमेव प्रायच्छत्। स्वर्णकाकस्तां भोजनमपि ताम्रभाजने एव अकारयत्।

शब्दार्थाः – तस्मिन् एव ग्रामे = अमुष्मिन् एव वसथे (उसी गाँव में), एकाऽपरा = एका अन्या (एक दूसरी), लुब्धा = लोभवशीभूता (लोभी), वृद्धा = जरठा (बुढ़िया), न्यवसत् = वासं करोति स्म (रहती थी), तस्या = अमुष्याः (उसकी), अपि = (भी), एका पुत्री = एका दुहिता (एक पुत्री), आसीत् = अवर्तत (थी), ईर्ष्णया = मत्सरेण (ईर्ष्या से), सा = (वह), तस्य स्वर्णकाकस्य = अमुष्य हेमवायसस्य (उस सोने के कौए के), रहस्यम् = गुप्तभेदं (रहस्य को), ज्ञातवती = बोधमाना (जान गई), सूर्यातपे = भानोः उष्णतायां (धूप में), तण्डुलान् = अक्षतान् (चावलों को),

निक्षिप्य = स्थिरीकृत्य (रखकर), तयापि = (उसने भी), स्वसुता = स्वपुत्री (अपनी पुत्री), रक्षार्थम् = रक्षायाः कृते (रक्षा के लिए), नियुक्ता = नियुक्ताम् अकरोत् (नियुक्त किया), तथैव = तेनैव प्रकारेण (उसी तरह), स्वर्णपक्षः काकः = हेमपक्षः वायसः (सुनहले पंखों वाले कौए ने), तण्डुलान् = अक्षतान् (चावलों को), भक्षयन् = खादन् (खाते हुए), तत्रैव = तस्मिन् एव स्थाने (वहीं), आकारयत् = आगन्तुम् अकथयत् (बुलाया), प्रातस्तत्र = प्रातःकालं तत्र (सुबह वहाँ), गत्वा = प्रस्थानं कृत्वा (जाकर), सा = (वह),

काकम् = वायसं (कौए की), निर्भसंयन्ती = निन्दां कुर्वन्ती (निन्दा करती हुई), प्रावोचत् = अवदत् (बोली), भो नीचकाकः = हे क्षुद्रवायसः (अरे नीच कौए), अहमागता = अहम् अत्र आगच्छम् (मैं यहाँ आ गयी हूँ), मह्यम् = मम कृते (मुझे), तण्डुलमूल्यम् = अक्षतानां मूल्यं (चावलों का मूल्य), प्रयच्छ = यच्छ (दो), काकः अब्रवीत् = वायसः अवदत् (कौआ बोला), अहम् = मैं, त्वत्कृते = तुभ्यम् (तुम्हारे लिए), सोपानम् अवतारयामि = सोपानम् अवतीर्णं करोमि (सीढ़ी उतारता हूँ।), तत्कथय = तु वद (तो बोलो), स्वर्णमयम् = हेममयं (सोने की बनी), रजतमयम् = रूप्यमयं (चाँदी की बनी),

ताम्रमयम् = लोहितायसमयं (ताँबे की बनी), वा = अथवा, गर्वितया = अभिमानेन (घमण्ड से), बालिकया = कन्यया (लड़की), प्रोक्तम् = अब्रवीत् (बोली), स्वर्णमयेन सोपानेन = हेमनिर्मितसोपानेन (सोने की बनी सीढ़ी से), अहम् आगच्छामि = अहम् आगमिष्यामि (मैं आऊँगी), परम् = परञ्च (लेकिन), स्वर्णकाकः = हेमवायसः (सुनहले कौए ने), तत्कृते = तस्यै (उसके लिए), ताम्रमयं सोपानमेव = लोहितायसमयं सोपानम् एव (ताँबे की सीढ़ी ही), प्रायच्छत् = अददात् (दी), स्वर्णकाकः = हेमवायसः (सुनहले कौए ने), ताम् = (उसको), भोजनमपि = अशनमपि (भोजन भी), ताम्रभाजने = लोहितायसपात्रे (ताँबे के बर्तन में), एव अकारयत् = एव पर्यवेषयत् (ही कराया/ही दिया)।

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ के ‘स्वर्णकाकः’ पाठ से उद्धृत है। यह पाठ श्रीपद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ नामक कथा-संग्रह से संकलित है।

प्रसंग – प्रस्तुत गद्यांश में वर्णन है कि एक लालंची महिला ने अपनी पुत्री से धूप में रखे चावलों की रक्षा करने को कहा। साथ ही सुनहले कौए के चावल खाने पर उससे उनका मूल्य लेने को भी कहा।

हिन्दी-अनुवाद – उसी गाँव में एक दूसरी लालची वृद्धा (बूढ़ी) औरत रहती थी। उसकी भी एक बेटी थी। ईर्ष्या से वह उस सुनहले कौए के रहस्य को जान गई। उसने भी धूप में चावलों को रखकर अपनी पुत्री को (उनकी) रक्षा करने के लिए नियुक्त किया। उसी तरह सुनहले पंखों वाले कौए ने चावलों को खाते हुए, उसे भी वहीं बुलाया। सुबह वहाँ जाकर वह कौए की निन्दा करती हुई बोली-अरे नीच कौए! मैं आ गयी, मुझे चावलों का मूल्य दो। कौआ बोला-मैं तुम्हारे लिए सीढ़ी उतारता हूँ, तो बोलो सोने की बनी, चाँदी की बनी अथवा ताँबे की बनी। घमण्ड से लड़की बोली-मैं सोने की बनी सीढ़ी से आऊँगी। लेकिन सुनहले कौए ने उसके लिए ताँबे की सीढ़ी ही दी। सुनहले कौए ने उसको भोजन भी ताँबे के बर्तन में ही कराया।

संस्कत-व्याख्याः

सन्दर्भ: – गद्यांशोऽयम् अस्माकं पाठ्यपुस्तकात् शेमुष्याः ‘स्वर्णकाकः’ पाठात् उद्धृतः। पाठोऽयं श्रीपद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम्’ इति कथासंग्रहात् सङ्कलितो वर्तते। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ से ‘स्वर्णकाकः’ पाठ से लिया गया है। यह पाठ श्री पद्मशास्त्री रचित ‘विश्वकथाशतकम्’ से संकलित है।)

प्रसङ्गः – वर्णितमत्र वर्तते यदेका लुब्धा स्त्री सूर्यातपे अक्षतान् निक्षिप्य स्वपुत्रीं तेषां रक्षार्थं नियुक्तवती। स्वर्णकाके च अक्षतान् खादिते तेषां मूल्यं ग्रहीतुम् अकथयत्। (इसमें वर्णन किया गया है कि एक लोभी स्त्री धूप में चावल रखकर अपनी बेटी को उनकी रखवाली के लिए नियुक्त करती है। स्वर्णकाक चावलों को खाता है और वह उनका मूल्य ग्रहण करने के लिए कहती है।)

व्याख्या: – तस्मिन् एव ग्रामे एका अन्या लोभान्विता वृद्धा स्त्री वसति स्म। तस्याः अपि एका दुहिता आसीत्। मत्सरेण सा वृद्धा तस्य हेमवायसस्य रहस्यम् अजानीत्। सा अपि सूर्यातपे अक्षतान् स्थिरीकृत्य स्वपुर्वी तेषां रक्षार्थं नियुक्ताम् अकरोत्। तथैव हेमवायसः तण्डुलान् खादन् तामपि तत्रैव आगन्तुम् अकथयत् सा (बालिका) प्रातः तत्र प्रस्थानं कृत्वा काकस्य निन्दा कुर्वन्ती अवदत् यद् भो अधमकाक! अहमत्र उपस्थिता अस्मि। मम कृते अक्षतानां मूल्यं देहि। काकः अवदत् यत् अहं तुभ्यं सोपानम् अवतारयामि, कथय तावत् स्वर्णमयं, रूप्यमयं ताम्रमयं वा।

गर्वयुक्ता सा बालिका प्रत्यवदत् यदहं स्वर्णमयेन सोपानेन आगमिष्यामि। परं स्वर्णकाकः तस्यै ताम्रसोपानमेव अददात्। स्वर्णकाकः तस्यै अशनमपि ताम्रपात्रे एव पर्यवेषयत्। (उसी गाँव में एक दूसरी लोभी बुढ़िया रहती थी। ईर्ष्या के कारण वह बुढ़िया स्वर्णकाक के रहस्य को जानती थी। उसने भी धूप में चावल रखकर अपनी बेटी को रखवाली के लिए नियुक्त कर दिया। उसी प्रकार सोने का कौवा चावलों को खाते हुए उसे भी आने के लिए कह गया।

वह लड़की भी प्रातः वहाँ प्रस्थान करके कौवे की निन्दा करती हुई बोली-अरे नीच कौवे; मैं यहाँ उपस्थित हो गई हूँ। मेरे लिए चावलों का मूल्य दो। कौआ बोला कि मैं तेरे लिए सीढ़ी उतारता हूँ, बोलो तो सोने की चाँदी की अथवा ताँबे की? गर्वयुक्त उस लड़की ने उत्तर दिया कि मैं सोने की सीढ़ी से ही आऊँगी। लेकिन स्वर्णकाक ने उसके लिए ताँबे की सीढ़ी दी। स्वर्ण काक ने उसके लिए भोजन भी ताँबे की थाली में दिया।)

अवबोधन कार्यम

प्रश्न 1.
एकपदेन उत्तरत- (एक शब्द में उत्तर दीजिए-)
(क) निर्धारित स्थान प्राप्य लुब्धायाः वृद्धाया पुत्री काकं केन शब्देन समबोधयत्।
(निर्धारित स्थान पर पहुँच कर लोभी वृद्धा की बेटी ने कौवे को किस शब्द से संबोधित किया?)
(ख) सा कस्य रहस्यं न ज्ञातवती? (वह किसके रहस्य को नहीं जान सकी?)

प्रश्न 2. पूर्णवाक्येन उत्तरत- (पूरे वाक्य में उत्तर दीजिए-)
(क) बालिका स्वर्णकाकस्य रहस्यं कस्मात् न ज्ञातवती? (बालिका स्वर्णकाक के रहस्य को क्यों नहीं जान सकी?)
(ख) बालिका निर्भत्सयन्ती काकं किं प्रावोचत्? (बालिका ने निन्दा करते हुए कौवा को क्या कहा?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) ‘पुत्री’ इति पदस्य पर्यायवाचि पदं गद्यांशात् अन्विष्य लिखत।
(‘पुत्री’ पद का पर्यायवाची पद गद्यांश से ढूँढ़ कर लिखिए।)
(ख) ‘तस्मिन्नेव ग्रामे’ एतयोः पदयोः किं विशेषणपदम् ?
(तस्मिन्नेव ग्रामे’ इनमें विशेषण पद कौनसा है?)
उत्तराणि :
(1) (क) नीच काक ! (नीच कौआ।)।
(ख) स्वर्णकाकस्य। (सोने के कौवे का)।

(2) (क) ईय॑या बालिका स्वर्णकाकस्य रहस्यं न ज्ञातवती। (ईर्ष्या के कारण बालिका स्वर्णकाक के रहस्य को न जान सकी।)
(ख) सा प्रांवोचत्-‘भो नीचकाक ! अहम् आगता मह्यं तण्डुल मूल्यं प्रदत्य। (वह बोली- अरे नीच कौवे! मैं आ गई हूँ, मेरे चावलों का मूल्य दो।)

(3) (क) सुता (बेटी)।
(ख) तस्मिन् (उसमें)।

6. प्रतिनिवृत्तिकाले स्वर्णकाकेन कक्षाभ्यन्तरात् तिम्रः मञ्जूषाः तत्पुरः समुत्क्षिप्ताः। लोभाविष्टा सा बृहत्तमा मञ्जूषां गृहीतवती। गृहमागत्य सा तर्षिता यावद् मञ्जूषामुद्घाटयति तावत् तस्यां भीषणः कृष्णसर्या विलोकितः। लुब्धया बालिकया लोभस्य फलं प्राप्तम्। तदनन्तरं सा लोभं पर्यत्यजत्।

शब्दार्था: – प्रतिनिवत्तिकाले = प्रत्यागमनस्य समये (वापस लौटते समय), स्वर्णकाकेन = हेमवायसेन (सोने के कौए द्वारा), कक्षाभ्यन्तरात् = कोष्ठस्य गर्भात् (कमरे के अन्दर से), तिस्रः = तीन, मञ्जूषाः = पेटिकाः (सन्दूकें/पेटियाँ), तत्पुरः = तस्याः अग्रे (उसके सामने), समुत्क्षिप्ताः = निक्षिप्ताः (रखी गईं), लोभाविष्टा = लोभवशीभूता (लोभ से घिरी), सा = (उसने), बृहत्तमाम् = विशालतमा (सबसे बड़ी), मञ्जूषाम् = पेटिकां (सन्दूक/पेटी), गृहीतवती = ग्रहणम् अकरोत् (ग्रहण की/ली),

गृहमागत्य = गेहम् आगत्य (घर आकर), सा = (उसने), हर्षिता = प्रसन्ना भवन्ती (प्रसन्न होती हुई), यावद् = यस्मिन्नेव क्षणे (जैसे ही), मञ्जूषामुद्घाटयति = पेटिकायाः भेदनम् अकरोत् (सन्दूक/पेटी को खोला), तावत् = तद्वत् एव (वैसे ही), तस्याम् = (उसमें), भीषणः = भयंकरः (भयंकर), कृष्णसर्पः = श्यामः भुजगः (काले साँप को), विलोकितः = अपश्यत् (देखा), लुब्धया बालिकया = लोभवशीभूतया बालिकया (लालची लड़की को), लोभस्य फलम् = परद्रव्याभिलाषस्य परिणाम (लोभ का फल), प्राप्तम् = (प्राप्त हो गया), तदनन्तरम् = तत्समयपश्चात् (उसके पश्चात्), सा = (उसने), लोभम् = परद्रव्याभिलाषां (लोभ को/लालच को), पर्यत्यजत् = अत्यजत् (छोड़ दिया)।

हिन्दी-अनुवादः

सन्दर्भ – प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक ‘शेमुषी’ के ‘स्वर्णकाकः’ पाठ से उद्धृत है। यह पाठ श्रीपद्मशास्त्री द्वारा रचित ‘विश्वकथाशतकम्’ कथा-संग्रह से संकलित है।

प्रसंग – प्रस्तुत गद्यांश में लड़की द्वारा कौए से सबसे बड़ी सन्दूक लेने, लोभ का फल प्राप्त करने तथा लालच का त्याग करने का वर्णन है।

हिन्दी-अनवाद – (घर) वापस लौटने के समय सनहले कौए ने कमरे के अन्दर से (लाकर) तीन पेटियाँ बालिका के सामने रखी। लोभ से घिरी लड़की ने सबसे बड़ी सन्दूक ग्रहण की। घर आकर उसने प्रसन्न होते हुए जैसे ही संदूक को खोला वैसे ही उसमें भयंकर काले साँप को देखा। इस प्रकार उस लड़की को लोभ का फल प्राप्त हो गया। उसके पश्चात् उसने लोभ छोड़ दिया।

संस्कत-व्यारव्याः

सन्दर्भ: – प्रस्तुतगद्यांशः अस्माकं पाठ्यपुस्तकात् शेमुष्याः ‘स्वर्णकाकः’ पाठात् उद्धृतः। पाठोऽयं श्रीपद्मशास्त्रिणा विरचितात् ‘विश्वकथाशतकम्’ इति कथासंग्रहात् सङ्कलितो वर्तते। (प्रस्तुत गद्यांश हमारी पाठ्यपुस्तक शेमुषी के ‘स्वर्णकाकः’ पाठ से लिया गया है। यह पाठ श्री पदम्शास्त्री रचित ‘विश्वकथाशतकम्’ कथा संग्रह से संकलित है।)

प्रसङ्गः – गद्यांशोऽयं वर्णयति यद् लुब्धा बालिका लोभस्य फलं प्राप्तम् अकरोत्। (यह गद्यांश वर्णित करता है कि लोभी बालिका लोभ का फ़ल पाती है।)

व्याख्याः – प्रत्यागमनस्य समये स्वर्णकाक: कोष्ठस्य गर्भात् तिम्रः पेटिकाः बालिकायाः समक्षं निक्षिप्तवान्। लुब्धा बालिका विशालतमा पेटिकाम् अग्रहीत्। गेहम् आगता प्रसन्ना भवन्ती सा यावदेव पेटिकाम् उद्घाटयत् तावदेव अन्तः स्थितं भयङ्करम् कृष्णसर्पम् अपश्यत्। एवं सा बालिका लोभस्य फलं प्राप्तम् अकरोत्। तत्पश्चात् सा लोभम् अत्यजत्। (लौटते समय स्वर्ण काक ने कमरे के अन्दर से लाकर तीन पेटियाँ बालिका के सामने रख दी। लोभी लड़की ने सबसे बड़ी पेटी ली। घर आई हई उसने जब पेटी को खोला तो उसके अन्दर एक भयंकर काला नाग देखा। इस प्रकार उस बालिका ने लोभ का फल प्राप्त किया। इसके बाद उसने लोभ त्याग दिया।)

अवबोधन कार्यम्

प्रश्न 1.
एकपदेन उत्तरत – (एक शब्द में उत्तर दीजिए-)
(क) लोभाविष्टा कन्या कीदृशी मञ्जूषां गृहीतवती? (लोभी कन्या ने कैसी मञ्जूषा ग्रहण की?)
(ख) लुब्धया बालिकया कस्य फलं प्राप्तम्? (लोभी बालिका ने किसका फल प्राप्त किया?)

प्रश्न 2.
पूर्णवाक्येन उत्तरत- (पूरे वाक्य में उत्तर दीजिए-)
(क) मञ्जूषाम् उद्घाट्य सा किम् अपश्यत् ? (मञ्जूषा को खोलकर उसने क्या देखा?)
(ख) काकः तिस्त्रः मञ्जूषा कदा आनयत्? (कौआ तीन मञ्जूषाएँ कब लाया?)

प्रश्न 3.
यथानिर्देशम् उत्तरत-(निर्देशानुसार उत्तर दीजिए-)
(क) ‘तदनन्तरं सा लोभं पर्यत्यजत्’ अत्र सा इति सर्वनामपदं कस्य स्थाने प्रयुक्तम्?
(यहाँ ‘सा’ सर्वनाम पद किस स्थान पर प्रयुक्त हुआ है।)
(ख) ‘कृष्णसर्पो’ अत्र विशेष्य पदं किम्? (‘कृष्णसर्पो’ यहाँ विशेष्य पद क्या है?)
उत्तराणि :
(1) (क) वृहत्तमाम्। (सबसे बड़ी को)।
(ख) लोभस्य (लोभ का)।
(2) (क) मञ्जूषाम् उद्घाट्य सा कृष्ण सर्पमपश्यत्। (मंजूषा को खोलकर उसने काला साँप देखा।)
(ख) प्रतिनिवृत्तिकाले स्वर्णकाकः तिस्रः मञ्जूषाः आनयत्। (लौटते समय स्वर्णकाक तीन पेटियाँ लाया।)
(3) (क) लुब्धा बालिकाया। (लोभी बालिका के स्थान पर।)
(ख) ‘सर्पः’ अत्र विशेष्य पदम्।

JAC Board Class 9th Social Science Notes History Chapter 5 Pastoralists in the Modern World

→  Introduction

• Pastoralism is a way of keeping animals such as cattle, sheep, camels or goats, and involves moving from one place to another in search of water and food.
• Pastoralism has been important in societies like India and Africa for years.

→ Pastoral Nomads and their Movements in the Mountains

• Nomads are people who do not live at one place, but move from one place to another to earn their living.
• The Gujjar Bakarwals of Jammu and Kashmir are great herders of goat and sheep.
• In winter, when the high mountains were covered with snow, the Gujjars lived along with their herds in the low hills of the Shiwalik range.
• By the end of April, they began their northern march for their summer grazing grounds. They crossed the Pir Panjal passes and entered the valley of Kashmir.
• By the end of September, the Bakarwals were on the move again, this time on their downward journey, back to their winter base. When the high mountains were covered with snow, the herds were grazed in the low hills.
• In a different area of the mountains, the Gaddi shepherds of Himachal Pradesh had a similar cycle of seasonal movement.
• This pattern of cyclical movement between summer and winter pastures was typical of many pastoral communities of the Himalayas, including the Bhotiyas, Sherpas and Kinnauris. All of them had to adjust to seasonal changes and make effective use of available pastures in different places.

→ On the Plateaus, Plains and Deserts

• Not all pastoralists operated in the mountains. They were also to be found in the pla-teaus, plains and deserts of India.
• Dhangars were an important pastoral community of Maharashtra. Most of them were shepherds. Some were blanket
  weavers. While others were buffalo herders.
• The Dhangars stayed in the central plateau of Maharashtra during the monsoon. Nothing but dry crops like bajra could be sown here.
• By October, the Dhangars harvested their bajra and started on their move to west. After a march of about a month, they reached the Konkan.
• With the onset of the monsoon, the Dhangars left the Konkan and the coastal areas with their flocks and returned to their settlements on the dry plateau.
• Other pastoral communities of Karnataka and Andhra Pradesh were the Gollas (herded cattle), the Kurumas and Kurubas (reared sheep and goats and sold woven blankets).
• Banjaraswere yet another well-known group of graziers. They were found in the vil-lages of Uttar Pradesh, Punjab, Rajasthan, Madhya Pradesh and Maharashtra.
• In the deserts of Rajasthan, lived the Raikas. They combined cultivation within pastoralism.
• One group of Raikas known as the Maru (desert) Raikas herded camels and another group reared sheep and goats.

→ Colonial Rule and Pastoral Life

• Under colonial rule, the life of Pastoralists changed dramatically. Their grazing grounds shrank, their movements were regulated, and the revenue they had to pay increased. Their agricultural stock declined and their trades and crafts were adversely affected.
• The colonial government wanted to transform all grazing lands into cultivated farms.
• By expanding cultivation, it could increase its revenue collection.
• Expansion of cultivation inevitably meant the decline of pastures and a problem for pastoralists.
• The Forest Acts made by the British Government changed the lives of pastoralists. Some
  forest which produced commercially valuable timber like ‘deodar’ or ‘sal’ were declared as ‘reserved’. .
• In the reserved forests, no pastoral activity was allowed, and in the protected forests, their activities were strictly restricted.
• In 1871, the British Government in India passed the Criminal Tribes Act. This act classified communities of craftsmen, traders and pastoralists as Criminal Tribes.
• As a result of this Act, these communities were expected to live only in notified vil¬lage settlements and they were not allowed to move without a permit from the British government.
• In the mid nineteenth century, Grazing tax was introduced by British Government in most pastoral lands of India.
• In order to increase income, the British Government imposed tax even on animals. The tax per head of cattle went up rapidly and the system of collection was made increasingly efficient.
• By the decade of1880s the government began collecting taxes directly from the pastoralists. To enter a grazing tract, the pastoralists had to show their pass and pay the tax.

→ How Did these Changes Affect the Lives of Pastoralists

• Wasteland Rules, Forest Acts, Criminal Tribes Act and imposition of grazing tax affected the lives of pastoralists adversely. These measures led to the serious shortage of pastures, as grazing lands were turned into cultivable land.
• The shepherds and cattle herders could no longer freely graze their cattle in the forests.
• Nomadic people had to move frequently from one place to another in search of pastures.
• Animal stock declined as under-fed cattle died in large numbers during droughts and famines.

→ How Did the Pastoralists Cope with these Changes?

• Pastoralists coped up with the changes in a variety of ways. Some pastoralists reduced the number of cattle in their herds, since there was not enough pasture to feed large numbers.
• Some pastoralists discovered new pastures when movement to old grazing grounds became difficult.
• Over the years, some richer pastoralists began buying land and settling down, giving up their nomadic life.
• Many poor pastoralists borrowed money from moneylenders to survive. Some of them became labourers, working on fields or in small towns. Yet, pastoralists not only continue to survive in many regions but their numbers have also expanded over recent decades.
• Many ecologists believe that in dry regions and in the mountains, pastoralism is still ecologically the most practical way of life.
• Such changes on pastoral communities were imposed not only in our country, but also all over the world.

→ Pastoralistn in Africa

• Africa is a continent where over half the world’s pastoral population lives.
• Even today, over 22 million Africans depend on some forms of pastoral activities for their livelihood.
• The different pastoral communities of Africa are Bedouins, Berbers, Maasai, Somali, Turkna and Boran.
• Most of them lived in semi-arid grasslands or arid deserts where rain fed agriculture is difficult.
• They raise cattle, camels, goats, sheep and donkeys and they sell milk, meat, animal skin and wool. Some of them earn through trade and transport.

→  Where have the Grazing Lands Gone?

• The Maasai are nomadic and pastoral people who depend on milk and meat for livelihood.
• The Maasai cattle herders live primarily in East Africa : 3,00,000 in Southern Kenya and another 1,50,000 in Tanzania.
• The new colonial laws and regulations took away their lives in times of drought and even reshaped their social relationships.
• One of the problems that Maasais have faced is the continuous loss <?f their grazing lands.
• In 1885, under colonial rule, Maasai land was cut into half with an International boundary between British Kenya and German Tonganyika. The Maasais lost about 60 per cent of their pre-colonial lands.
• As cultivation expanded, pasturelands were turned into cultivated fields.
• Large areas of grazing lands were also turned into game reserves like the Maasai Mara in Kenya and Serengeti Park in Tanzaniya; pastoralists were not allowed to enter these reserves.

→ The Borders are Closed

• Pastoral groups were forced to live within the boundaries of special reserves.
• They were not allowed to move out with their stock without special permits. They were not even allowed to trade and enter the markets in white areas.
• These restrictions adversely affected both their pastoral and trading activities. Earlier, pastoralists not only looked after animal herds, but they also traded in various products.

→ When Pastures Dry

• The Maasais were forced to live in drought-prone areas, as a result of this, large num-bers of Maasai cattle died of starvation and diseases. There was a severe decline in the animal stock of Maasais.

→ Not All were Equally Affected

• The colonial rules had unequal effects on elders and warrior groups of Maasai society.
• The British imposed various restrictions on raiding and warfare. Thus, the traditional authority of both elders and warriors was negatively affected.
• The chiefs appointed by the colonial government collected wealth overtime. They started to live in towns and got involved in trades. Their families stayed back in villages to look after land and animals.
• The poor pastoralists did not have the resources to survive in bad times and thus they were forced to do odd jobs like charcoal burners, workers in road and building construction etc.

→ Conclusion

• Pastoral communities in different parts of the world are affected in a variety of different way by changes in the modem world. New laws and new borders affect the patterns of their movement.
• They change the path of their annual movements reduce their cattle numbers, pressurise for rights to enter new areas.
• They put political pressure on the government for relief, subsidy and other forms of support and demand a right in the management of forests and water resources.
• Economists and environmentalists have increasingly come to recognise that pastoral nomadism is a form of life that is perfectly suited to many hilly and dry regions of the world even today.

→ Important Dates and Related Events

• 1871: The Criminal Tribes Act was passed by the colonial government in India.
• 1850s- 1880s: The right to collect the tax was auctioned out to contractors.
• 1880s: The government began collecting taxes directly from the pastoralists. Each of them was given a pass.
• 1885: The Maasailand (Africa) was cut into two with an international boundary between British Kenya and German Tanganyika.

→ Nomads: People who move from one place to another to earn their living.

→ Gujjar Bakarwals: A Nomadic tribe of Jammu and Kashmir.

→ Kafila: Movement of a large number of households on a long journey.

→ Gaddi: The shepherd community of Himachal Pradesh.

→ Bhabar: A dry forested area below the foothills of Garhwal and Kumaun.

→ Bugyal: Vast meadows in the high mountains.

→ Bhotiyas, Sherpas, Kinnauris: Pastoral communities of the Himalayan region.

→ Dhars : Pasture land on the high mountains.

→ Dhangars : Pastoral community of Maharashtra.

→ Kharif: The autumn crop, usually harvested between September and October.

→ Rabi: The spring crop, usually harvested after March.

→ Stubble: Lower ends of grain stalks left in the grounds after harvesting.

→ Gollas,Kurumas,Kurubas: Pastoral communities in Karnataka and Andhra Pradesh.

→ Raikas: A pastoral tribe in Rajasthan.

→ Banjaras: A group of graziers found in U.P., Punjab, Rajasthan, Madhya Pradesh and Maharashtra.

→ Maru: A local name for Rajasthan’s desert.

→ Geneologist: A person who recounts the history of the community by narrating the facts orally.

→ Pastures: Tracts of land that are covered with a variety of grasses, roots and herbs, and wild flowers.

→ Pastoralists: A group of people that earns its living by the rearing of animals like goats, sheep, buffaloes, cows and camels.

→ Customary rights : Rights that people are used to by custom and tradition.

→ Bedouins, Berbers, Maasai, Somali, Boran and Turkang: Pastoral communities of Africa.

JAC Class 9 Social Science Notes

Jharkhand Board JAC Class 10 Maths Solutions Chapter 6 Triangles Ex 6.5 Textbook Exercise Questions and Answers.

JAC Board Class 10 Maths Solutions Chapter 6 Triangles Exercise 6.5

Question 1.
Sides of triangles are given below, Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse:
1. 7 cm, 24 cm, 25 cm
2. 3 cm, 8 cm, 6 cm
3. 50 cm, 80 cm, 100 cm
4. 13 cm, 12 cm, 5 cm
Solution :
1. 7 cm, 24 cm, 25 cm.
Here, the longest side is 25 cm.
25² = 625 and 7² + 24² = 49 + 576 = 625
∴ 25² = 7² + 24²
Here, the square of the longest side equals the sum of squares of the other two sides. Hence, the triangle with sides 7 cm, 24 cm and 25 cm is a right triangle and the length of its hypotenuse, is 25 cm.

2. 3 cm, 8 cm, 6 cm
Here, the longest side is 8 cm.
8² = 64 and 3² + 6² = 9 + 36 = 45
∴ 8² ≠ 3² + 6²
Hence, the triangle with sides 3 cm, 8 cm and 6 cm is not a right triangle.

3. 50 cm, 80 cm, 100 cm
Here, the longest side is 100 cm.
100² = 10000 and
50² + 80² = 2500 + 6400 = 8900
∴ 100² ≠ 50² + 80²
Hence, the triangle with sides 50 cm, 80 cm and 100 cm is not a right triangle.

4. 13 cm, 12 cm, 5 cm
Here, the longest side is 13 cm.
13² = 169 and 12² + 5² = 144 + 25 = 169
∴ 13² = 12² + 5²
Here, the square of the longest side equals the sum of squares of the other two sides. Hence, the triangle with sides 13 cm. 12 cm and 5 cm is a right triangle and the length of its hypotenuse is 13 cm.

Question 2.
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM² = QM. MR.
Solution :

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR.
∴ ΔRMP ~ ΔPMQ ~ ΔRPQ (Theorem 6.7)
Now, ΔRMP ~ ΔPMQ
∴ \(\frac{PM}{QM}=\frac{RM}{PM}\)
∴ PM² = QM. MR

Question 3.
In the given figure, ABD is a triangle right-angled at A and AC ⊥ BD. Show that
1. AB² = BC.BD
2. AC² = BC.DC
3. AD² = BD.CD
Solution :

ABD is a triangle right angled at A and AC ⊥ BD.
∴ ΔBCA ~ ΔACD ~ ΔBAD (Theorem 6.7)
1. ΔBCA ~ ΔBAD
∴ \(\frac{AB}{DB}=\frac{CB}{AB}\)
∴ AB² = BC. BD

2. ΔBCA ~ ΔACD
∴ \(\frac{AC}{DC}=\frac{BC}{AC}\)
∴ AC² = BC. DC

3. ΔACD ~ ΔBAD
∴ \(\frac{AD}{BD}=\frac{CD}{AD}\)
∴ AD² = BD . CD

Question 4.
ABC is an isosceles triangle right angled at C. Prove that AB² = 2AC².
Solution :
ABC is an isosceles triangle right angled at C.
Hence, AB is the hypotenuse and the other two sides are equal, i.e., BC = AC
In ΔABC, ∠C = 90°

∴ By Pythagoras theorem,
AB² = BC² + AC²
∴ AB² = AC² + AC² (∵ BC = AC)
∴ AB² = 2AC²

Question 5.
ABC is an isosceles triangle with AC = BC. If AB² = 2AC², prove that ABC is a right triangle.
Solution :
In ΔABC, AC = BC and AB² = 2AC²
AB² = 2AC²
∴ AB² = AC² + AC²
∴ AB² = AC² + BC² (∵ AC = BC)
Hence, by the converse of Pythagoras theorem, ΔABC is right triangle in which ∠C is a right angle.

Question 6.
ABC is an equilateral triangle of side 2a. Find each of its altitudes.
Solution :

In ΔABC, AB = BC = CA = 2a.
Let AD be its altitude
∴ ∠ADB = ∠ADC = 90°
In ΔADB and ΔADC,
∠ADB = ∠ADC = 90°
AB = AC
AD = AD
∴ By RHS criterion,
= ΔADC
∴ BD = CD
But, BD + CD = BC
∴ BD = CD = \(\frac{1}{2}\)BC = \(\frac{1}{2}\)(2a) = a
Now, in ΔADB, ∠D = 90°
∴ By Pythagoras theorem,
AB² = AD² + BD²
∴ (2a)² = AD² + (a)²
∴ 4a² – a² = AD²
∴ AD² = 3a²
∴ AD = \(\sqrt{3}\)a
All the altitudes of an equilateral triangle are equal.
Hence, each of the altitudes of equilateral ΔABC with side 2a is \(\sqrt{3}\)a.

Question 7.
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Solution :
Given: ABCD is a rhombus.
To prove : AB² + BC² + CD² + DA² = AC² + BD²

Proof: ABCD is a rhombus.
∴ AB = BC = CD = DA ……………(1)
Let its diagonals AC and BD intersect at M.
Then, MA = MC = \(\frac{1}{2}\)AC.
MB = MD = \(\frac{1}{2}\)BD and
∠AMB = ∠BMC = ∠CMD = ∠DMA = 90°
In ΔAMB, ∠AMB = 90°
∴ AB² = MA² + MB² (Pythagoras theorem)
∴ AB² = (\(\frac{AC}{2}\))² + (\(\frac{BD}{2}\))²
∴ AB² = (\(\frac{AC}{2}\))² + (\(\frac{BD}{2}\))²
∴ 4AB² = \(\frac{\mathrm{AC}^2}{4}+\frac{\mathrm{BD}^2}{4}\)
∴ 4AB² = AC² + BD²
∴ AB² + AB² + AB² + AB² = AC² + BD²
∴ AB² + BC² + CD² + DA² = AC² + BD²

Question 8.
In the given figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that:
1. OA² + OB² + OC² – OD² – OE² – OF² = AF² + BD² + CE²
2. AF² + BD² + CE² = AE² + CD² + BF².
Solution :

Join OA, OB and OC.
Here, in ΔOFA and ΔOFB, ∠F = 90°, in ΔODB and ΔODC, ∠D = 90° and in ΔOEC and ΔOEA. ∠E = 90°.
Then, Pythagoras theorem is applicable in all the triangles.
1. In ΔOFA, ∠F = 90°
∴ OA² = OF² + AF²
∴ AF² = OA² – OF² …………..(1)
In ΔODB, ∠D = 90°
∴ OB² = OD² + BD²
∴ BD² = OB² – OD² …………..(2)
In ΔOEC, OE² + CE²
∴ CE² = OC² – OE² …………..(3)
Adding (1), (2) and (3).
AF² + BD² + CE² = OA² – OF² + OB² – OD² + OC² – OE²
∴ OA² + OB² + OC² – OD² – OE² – OF² = AF² + BD² + CE²

2. AF² + BD² + CE² = OA² + OB² + OC² – OD² – OE² – OF²
∴ AF² + BD² + CE² = (OA² – OE²) + (OB² – OF²) + (OC² – OD²)
∴ AF² + BD² + CE² = AE² + BF² + CD² (∵ ΔOAE, ΔOBF and ΔOCD are right triangles)
∴ AF² + BD² + CE² = AE² + CD² + BF²

Question 9.
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
Solution :

Here, AB is the wall with window at point A and AC is the ladder.
Then, AC = 10m and AB = 8 m.
In ΔABC, ∠B = 90°.
∴ AC² = AB² + BC² (Pythagoras theorem)
∴ 10² = 8² + BC²
∴ BC² = 10² – 8²
∴ BC² = 100 – 64
∴ BC² = 36
∴ BC = 6 m
Thus, the distance of the foot of the ladder from the base of the wall is 6 m.

Question 10.
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Solution :

Here, AB is the vertical pole in which the guy wire is attached at point A and AC is the guy wire and 18 m the stake is attached to its end C.
Then, AC = 24 m and AB = 18 m.
In ΔABC, ∠B = 90°
∴ AC² = AB² + BC² (Pythagoras theorem)
∴ 24² = 18² + BC²
∴ BC² = 576 – 324
∴ BC² = 252
∴ BC² = 4 × 9 × 7
∴ BC = 2 × 3 × \(\sqrt{7}\)
∴ BC = 6\(\sqrt{7}\) m
Thus, the stake should be driven 6\(\sqrt{7}\)m far from the base of the pole, so as to make the wire taut.

Question 11.
An airplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another airplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1\(\frac{1}{2}\) hours?
Solution :

Here, A is the airport, B is the position of the first plane flying due north after 1\(\frac{1}{2}\) hours and C is the position of the second c- plane flying due west after 1\(\frac{1}{2}\) hours.
[Note: For the sake of simplicity, we consider that both the planes are flying at the same height and point A representing the airport is also imagined to be at the same height.]
Then, AB = distance covered by the first plane in 1\(\frac{1}{2}\) hours
= Speed × Time
= 1000 × \(\frac{3}{2}\)
= 1500 km
Similarly, AC = distance covered by the second plane in 1\(\frac{1}{2}\) hours
= Speed × Time
= 1200 × \(\frac{3}{2}\)
= 1800 km
Also, ∠BAC is the angle formed by north direction and west direction.
Hence ∠BAC = 90°
Now, in ΔABC, ∠A = 90°
∴ BC² = AB² + AC² (Pythagoras theorem)
∴ BC² = (1500)² + (1800)²
∴ BC² = 22500 + 32400
∴ BC² = 54900
∴ BC = \(\sqrt{100 \times 9 \times 61}\)
∴ BC = 300\(\sqrt{61}\) km
Thus, the two planes will be 300\(\sqrt{61}\) km apart from each other after 1\(\frac{1}{2}\) hours.

Question 12.
Two poles of heights 6m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Solution :

Here, AB and CD are two erect poles of height 6 m and 11 m respectively.
The distance between the feet of the poles is 12 m.
Then, AB = 6 m, BD = 12 m, CD = 11 m, ∠B = 90° and ∠D = 90°.
Draw AE || BC.
Then, in quadrilateral ABDE.
∠B = ∠D = ∠E = ∠A = 90°.
Hence, ABDE is a rectangle.
∴ ED = AB = 6m and AE = BD = 12 m.
Then, CE = CD – DE = 11 – 6 = 5m
Now, in ΔAEC, ∠E = 90°.
∴ AC² = AE² + CE² (Pythagoras theorem)
∴ AC² = 12² + 5²
∴ AC² = 144 + 25
∴ AC² = 169
∴ AC = 13 m
Thus, the distance between the tops of the vertical poles is 13 m.

Question 13.
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE² + BD² = AB² + DE²
Solution :
In ΔABC, ∠C is a right angle, point D lies on CA and point E lies on CB.

Then, all the four triangles BCD, BCA, ECD and ECA are right triangles and in each of them C is a right angle.
Hence, Pythagoras theorem is applicable in all the four triangles.
In ΔECA, AE² = EC² + CA² ……………..(1)
In ΔBCD, BD² = BC² + CD² ……………..(2)
In ΔBCA, AB² = BC² + CA² ……………..(3)
In ΔECD, DE² = EC² + CD² ……………..(4)
Adding (1) and (2).
AE² + BD² = EC² + CA² + BC² + CD²
= (BC² + CA²) + (EC² + CD²)
= AB² + DE² [By (3) and (4)]
Thus, AE² + BD² = AB² + DE²

Question 14.
The perpendicular from A on side BC of a ΔABC intersects BC at D such that DB = 3CD (see the given figure). Prove that 2AB² = 2AC² + BC².
Solution :

DB = 3CD
∴ BC = DB + CD = 3CD + CD
∴ BC = 4CD …………..(1)
In ΔADB, ∠D = 90°
∴ AB² = AD² + DB² (Pythagoras theorem) …………..(2)
In ΔADC, ∠D = 90°
∴ AC² = AD² + CD² (Pythagoras theorem) …………..(3)
Subtracting (3) from (2),
AB² – AC² = (AD² + DB²) – (AD² + CD²)
∴ AB² – AC² = DB² – CD²
∴ AB² – AC² = (DB + CD) (DB – CD)
∴ AB² – AC² = (BC) (3CD – CD)
∴ AB² – AC² = (BC) (2CD)
Multiplying the equation by 2, we get
2AB² – 2AC² = (BC) (4CD)
∴ 2AB² – 2AC² = (BC) (BC)
∴ 2AB² = 2AC² + BC² [By (1)]

Question 15.
In an equilateral triangle ABC, D is a point on side BC such that BD = \(\frac{1}{3}\)BC. Prove that 9AD² = 7AB².
Solution :
Given: In equilateral ΔABC, D is a point on BC such that BD = \(\frac{1}{3}\)BC.
To prove: 9AD² = 7AB²

Construction: Draw AM ⊥ BC, such that M lies on BC.
Proof: ΔABC is an equilateral triangle. Suppose, AB = BC = AC = a
In equilateral ΔABC, AM is an altitude.
∴ AM is a median.
∴ BM = \(\frac{1}{2}\)BC = \(\frac{1}{2}\)a
∴ BD = \(\frac{1}{3}\)BC. Hence, DC = \(\frac{2}{3}\)BC
BD = \(\frac{1}{3}\)BC = \(\frac{1}{3}\)a
DM = BM – BD = \(\frac{1}{2}\)a – \(\frac{1}{3}\)a = \(\frac{1}{6}\)a
In ΔAMB, ∠M = 90°
∴ AB² = AM² + BM²
∴ a² = AM² + \(\frac{1}{4}\)a²
∴ AM² = \(\frac{3}{4}\)a²
In ΔAMD, ∠M = 90°
∴ AD² = AM² + DM²

∴ 9AD² = 7a²
∴ 9AD2 = 7AB² (∵ AB = a)

Question 16.
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Solution :

ABC is an equilateral triangle in which AD is an altitude.
Let AB = BC CA- a units.
In an equilateral triangle, an altitude is a median also.
∴ AD is a median.
∴ BD = \(\frac{1}{2}\)BC = \(\frac{a}{2}\)units
In ΔADB, ∠D = 90°
∴ AB² = AD² + BD²
∴ (a)² = AD² + (\(\frac{a}{2}\))²
∴ a² = AD² + \(\frac{a^2}{4}\)
∴ \(\frac{3}{4}\)a² = AD²
∴ 3a² = 4AD²
∴ 3 (side)² = 4 (altitude)²

Question 17.
Tick the correct answer and justify: In ΔABC, AB = 6\(\sqrt{3}\) cm, AC = 12 cm and BC= 6 cm. The angle B is:
(A) 120°
(B) 60°
(C) 90°
(D) 45°
Solution :
In ΔABC, AB = 6\(\sqrt{3}\) cm = 10.38 cm (approx),
AC = 12 cm and BC = 6 cm
Here, AC is the longest side.
Then, 12² = 144 and
(6\(\sqrt{3}\))² + (6)² – 108 + 36 = 144
Thus, 12² = (6\(\sqrt{3}\))² + (6)²
Hence, by the converse of Pythagoras theorem, ΔABC is a right triangle in which the longest side AC is the hypotenuse and its opposite angle ∠B is a right angle.
Hence, the correct answer is (C) 90°.