Question

Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)^rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.

Answer 1

Given that

Construct a triangle of given data, BC = 6 cm, ∠B = 50° and ∠C = 60° and then a triangle similar to it whose sides are (2/3)^rd of the corresponding sides of ΔABC.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment Bc = 60°.

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

Step: III- With C as centre draw an angle ∠C = 60° which intersecting the line drawn in step II at A.

Step: IV- Joins AB and AC to obtain ΔABC.

Step: V -Below BC, makes an acute angle ∠CBX = 60°.

Step: VI -Along BX, mark off three points B₁, B₂ and B₃ such that BB₁ = B₁B₂ = B₂B₃

Step: VII -Join B₃C.

Step: VIII -Since we have to construct a triangle each of whose sides is two-third of the corresponding sides of ΔABC.

So, we take two parts out of three equal parts on BX from point B₂ draw B₂C' || B₃C, and meeting BC at C’.

Step: IX -From C’ draw C'A' || AC and meeting AB at A’

Thus, ΔA'BC' is the required triangle, each of whose sides is two third of the corresponding sides of ΔABC.