Question

Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)^th  of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.

Answer 1

Given that

AB = 5 cm, BC = 7 cm and ∠ABC = 50°

Construct a triangle similar to a triangle ABC such that each of sides is (5/7)^th of the corresponding sides of triangle ABC.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment AB = 5 cm.

Step: II- With B as centre and draw an angle ∠ABY = 50°.

Step: III- With B as centre and radius = BC = 7 cm, draw an arc, cut the line BY drawn in step II at C.

Step: IV- Joins AC to obtain ΔABC.

Step: V- Below AB, makes an acute angle ∠BAX = 60°.

Step: VI- Along AX, mark off seven points A₁, A₂, A₃, A₄, A₅, A₆ and A₇ such that AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆ = A₆A₇

Step: VII-Join A₇B.

Step: VIII- Since we have to construct a triangle each of whose sides is (5/7)^th of the corresponding sides of ΔABC.

So, we take five parts out of seven equal parts on AX from point A₅ draw A₅B' || A₇B and meeting AB at B’.

Step: IX- From B'draw B'C || BC and meeting AC at C’

Thus, ΔAB'C' is the required triangle, each of whose sides is (5/7)^th of the corresponding sides of ΔABC.