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 B 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 B₃C.
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.