Question

Construct a ΔABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct a triangle similar to this triangle whose sides are `3/4` of the corresponding sides of ΔABC.

Answer 1

Steps of Construction:

Step 1: Draw a line segment BC = 6.5 cm.

Step 2: With B as centre, draw an angle of 60°.

Step 3: With B as centre and radius equal to 4.5 cm, draw an arc, cutting the angle at A. 

Step 4: Join AB and AC.

Thus, ΔABC is obtained.

Step 5: Below BC, draw an acute ∠CBX.

Step 6: Along BX, mark of four points B₁, B₂, B₃, B₄, such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.   

Step 7: Join B₄C.

Step 8: From B₃, draw B₃D || B₄C, meeting BC at D.

Step 9: From D, draw DE || CA, meeting AB at E.

Thus, ΔEBD is the required triangle, each of whose sides is `3/4` the corresponding sides of ΔABC.