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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?
Solution
Steps of construction:
- Draw a line segment BC = 12 cm,
- From B draw a line AB = 5 cm which makes right angle at B.
- Join AC, ΔABC is the given right triangle.
- From B draw an acute ∠CBY downwards.
- On ray BY, mark three points B1, B2 and B3, such that BB1= B1B2 = B2B3.
- Join B3C.
- From point B2 draw B2N || B3C intersect BC at N.
- From point N draw NM || CA intersect BA at M. ΔMBN is the required triangle. ΔMBN is also a right-angled triangle at B.
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