Question

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor `2/3`. Is the new triangle also a right triangle?

Answer 1

Steps of construction:

1. Draw a line segment BC = 12 cm,

2. From 6 draw a line AB = 5 cm which makes right angle at B.

3. Join AC, ΔABC is the given right triangle.

4. From B draw an acute ∠CBY downwards.

5. On ray BY, mark three points B₁, B₂ and B₃, such that BB₁ = B₁B₂ = B₂B₃.

6. Join B₃ C.

7. From point B₂ draw B₂N || B₃C intersect BC at N.

8. From point N draw NM || CA intersect BA at M. ΔMBN is the required triangle. ΔMBN is also a right-angled triangle at B.