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 B_{1}, B_{2,} and B_{3,}

BB_{1}=B_{1}B_{2} =B_{2}B_{3}

6. Join B_{3} C

7. Draw B_{2}N||B_{3}C 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.

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