(Q30) Construct a triangle similar to the given △ABC, with its sides equal to

5

3

of the corresponding sides of the triangle ABC.

Solution :

Steps of construction :

1. Draw a ∆ with certain measures.

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

3. Locate points (B₁, B₂,...., B₈) on BX such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅ = B₅B₆ = B₆B₇ = B₇B₈

4. Join B₅, C

5. Draw a line parallel to B₅C through which it intersects extended at C'.

6. Draw a line parallel to through 'C' which meets BA produced at A'.

7. ∆A'BC' is the required triangle.