Question

Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)^th of the corresponding sides of ΔABC.

Answer 1

Given that

Construct a triangle of sides BC = 6 cm, AB = 4 cm and AC = 5 cm and then a triangle similar to it whose sides are (3/4)^th 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 AB = 4 cm.

Step: II- With A as centre and radius = AC = 5 cm, draw an arc.

Step: III -With B as centre and radius = BC = 6 cm, draw an arc, intersecting the arc drawn in step II at C.

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

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

Step: VI -Along AX, mark off four points A₁, A₂, A₃ and A₄ such that AA₁ = A₁A₂ = A₂A₃ = A₃A₄

Step: VII -Join A₄B.

Step: VIII -Since we have to construct a triangle each of whose sides is (3/4)^th of the corresponding sides of ΔABC.

So, we take three parts out of four equal parts on AX from point A₃ draw A₃B' || A₄B, 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 (3/4)^th of the corresponding sides of ΔABC.