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 AB = 5 cm. Construct a right angle SAB at point A.

2. Draw an arc of radius 12 cm with B as its centre to intersect SA at C.

3. Join BC to obtain ABC.

4. Draw a ray AX making an acute angle with AB, opposite to vertex C.

5. Locate 3 points, A₁, A₂, A₃ on line segment AX such that AA₁ = A₁A₂ = A₂A₃.

6. Join A₃B.

7. Draw a line through A₂ parallel to A₃B intersecting AB at B’.

8. Through B’, draw a line parallel to BC intersecting AC at C’.

9. Triangle AB’C’ is the required triangle.