Jharkhand Board JAC Class 9 Maths Important Questions Chapter 11 Constructions Important Questions and Answers.

## JAC Board Class 9th Maths Important Questions Chapter 11 Constructions

Question 1.

Construct an equilateral triangle if its altitude is 3.2 cm.

Solution :

Given: In an equilateral ΔABC, an altitude

AD = 3.2 cm

Required: To Construct an equilateral triangle ABC from the given data.

STEPS:

(i) Draw a line PQ

(ii) Construct a perpendicular bisector DE to PO.

(iii) Cut off DA = 3.2 cm from DE.

(iv) Construct ∠DAR = 30°.

The ray AR intersects PQ at B.

(v) Similarly, draw ∠DAC = 30.

The ray AC intersects PQ at C.

(vi) Join A with B and C.

We get the required ΔABC.

Question 2.

Construct a right-angled triangle whose hypotenuse measures 8 cm and one side is 6 cm.

Solution :

Given: Hypotenuse AC of a ΔABC = 8 cm and one side AB = 6 cm.

Required: To construct a right-angled ΔABC from the given data.

STEPS:

(i) Draw a line segment AC = 8 cm.

(ii) Mark the mid-point 0 of AC by doing perpendicular bisector of AC.

(iii) With O as centre and radius OA, draw a semicircle on AC.

(iv) With A as centre and radius equal to 6 cm, draw an arc, cutting the semicircle a B.

(v) Join A and B, B and C.

We get the required right-angled triangle ABC

Question 3.

Construct a ΔABC in which BC = 6.4 cm, altitude from A is 3.2 cm and the median bisecting BC is 4 cm.

Solution :

Given: One side BC = 6.4 cm, altitude AD = 3.2 cm and the median AL = 4 cm.

Required: To construct a ΔABC form the given data

STEPS:

(i) Draw BC = 6.4 cm

(ii) Bisect BC at L.

(iii) Draw EF || BC at a distance 3.2 cm for BC

(iv) With L as centre and radius equal to 4 cm, draw an arc, cutting EF at A

(v) Join A and B ; A and C, A and L.

We get the required triangle ABC

Question 4.

Construct a ΔABC in which ∠B = 30° and ∠C = 60° and the perpendicular from the vertex A to the base BC is 4.8 cm.

Solution :

Given: ∠B = 30°, ∠C = 60°, length of perpendicular from vertex A to be base BC = 4.8 cm.

Required: To construct a ΔABC from the given data.

STEPS :

(i) Draw any line PQ.

(ii) Take a point B on line PQ and construct ∠QBR = 30°

(iii) Draw a line EF || PQ at a distance of 4.8 cm from PQ, cutting BR at A.

(iv) Construct an angle ∠FAC = 60°, cutting PQ at C.

(v) Join A and C.

We get the required triangle ABC.

Question 5.

Construct a triangle ABC, the lengths of whose medians are 6 cm, 7 cm and 6 cm.

Solution :

Given: Median AD = 6 cm, median BE = 7 cm, median CF = 6 cm.

Required: To construct a AABC from the given data.

STEPS:

(i) Construct a ΔAPQ with AP = 6 cm, PQ = 7 cm and AQ = 6 cm.

(ii) Draw the medians AE and PF of ΔAPQ intersecting each other at G.

(iii) Produce AE to B such that GE = EB

(iv) Join B and Q and produce it to C, such that BQ = QC

(v) Join A and C. We get the required triangle ABC.