71. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc  of the corresponding sides of the first triangle.

Steps of Construction :

(i) Construct a ΔABC in which AB = 6 cm, AC = 4 cm, BC = 5 cm.
(ii)    At A draw an acute ∠BAX below base AB.
(iii)    Along AX mark off points A₁, A₂, A₃ such that AA₁ = A₁ A₁ = A₂ A₃.
(iv)    Join A₃B.
(v)    From A₂ draw A₂B’ || A₃B meeting AB at B’.
(vi)    From B’ draw B‘C’ || CB meeting AC at C’. Thus, ΔAB‘C’ is the required triangle, each of whose sides is (2/3)rd of the corresponding sides of the ΔABC.
Justification :

[From (i)]
[By Basic proportionality theorem)