Question

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.

Answer 1

Steps of Construction :

• Draw a line segment BC = 6 cm.
• At B, draw ∠CBY = 60°.
• From B draw an arc AB = 5 cm meeting BY at A. Join AC. Thus, ∆ABC was obtained.
• Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
• Along BX mark four points B₁, B₂, B₃, B₄ such that BB₄ = B₁B₂ = B₂B₃ = B₃B₄.
• Join B₄C.

• From B₃ draw B₃C’ ∥ B₄C meeting BC at C.
• From C’ draw C’A’ ∥ CA, meeting AB at A.

Then A’BC is the required triangle, each of whose side is 34 of corresponding sides of ∆ABC.