74. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are  of the corresponding sides of the triangle ABC.

Steps of Construction :

(i)    Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°.
(ii)    Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
(iii)    Along BX, mark off 4 points B₁, B₂, B₃ and B₄ on BX such that BB₁ = B₁B₂ = B₂ B₃ = B₃B₄.
(iv) Join B₄C and draw a line through B₃ parallel to B₄ C intersecting BC to C’.
(v) Draw a line through C’ parallel to the line CA to intersect BA at A’.



Then A ‘BC’ is the required triangle. Justification :


[By the Basic Proportionality Theorem]