(Q31) Construct a triangle of sides 4 cm, 5 cm and 6 cm. Then, construct a triangle similar to it,whose sides are 2/3 of the corresponding sides of the first triangle.

Solution :

B1B2B3BxCC'A'A4 cm5 cm6 cm

Steps of construction:

1. Draw ∆ABC with AB = 4 cm, BC = 5 cm and CA = 6 cm.

2. Draw a ray making an acute angle with BC on the side opposite to vertex A.

3. Mark three points B1, B2 and B3 on such that BB1 = B1B2 = B2B3.

4. Join B3C.

5. Draw a line parallel to B3C through B2 meeting at C'.

6. Draw a line parallel to BA through C' meeting at A'.

7. ∆A'BC' is the required triangle.