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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°.
Solution
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.
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