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, and then a triangle similar to it whose sides are of the corresponding sides of .

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment.

Step: II- With B as centre draw an angle.

Step: III- With C as centre draw an anglewhich intersecting the line drawn in step II at A.

Step: IV- Joins AB and AC to obtain.

Step: V -Below BC, makes an acute angle.

Step: VI -Along BX, mark off three points such that

Step: VII -Join.

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

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

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

Thus, is the required triangle, each of whose sides is two third of the corresponding sides of.