Question

Construct a triangle ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ∆ABC.

Answer 1

Given: A ∆ABC with ​ BC=7 cm, ∠B=60° and AB=6 cm

Steps of Construction

1. Draw a line segment AB = 6 cm.

2. With B as centre, draw ∠B=60°.

3. With B as centre and radius BC = 7 cm, draw an arc.

4. Join AC to obtain ∆ABC.

5. Below AB, make an acute angle ∠BAX.

6. Along AX, mark off four points  A₁, A₂, A₃ and A₄ such that AA₁=A₁A₂=A₂A₃=A₃A₄

7. Join A₄B

8. From A₃, draw A₃B'∥A₄B.

9. From B', draw B'C'∥BC.

Thus, ∆AB'C' is the required triangle with each of its side `3/4` times the size of the corresponding sides of ∆ABC.