Draw a right ∆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?

Steps of construction

1. Draw a line BC=12 cm.

2. Draw a line AB=5 cm

3. Join AC.

4. Draw an acute CBY downwards.

5.On ray BY, mark three-point B1, B2, and B3,

BB1=B1B2 =B2B3

6. Join B3 C

7. Draw B2N||B3C intersect BC at N.

8. Draw NM||CA intersect BA at M.

∆MBN is the required triangle.

Hence, ∆MBN is also a right-angled triangle at B.