Question

Construct a ∆ABC, in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct a triangle similar to this triangle whose sides are $\frac{3}{4}$ the corresponding sides of ∆ABC.

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^o.
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, △ ABC is obtained .
Step 5. Below BC, draw an acute $\angle CBX$.
Step 6. Along BX, mark off four points B₁, B₂, B₃, B₄, such that BB₁ = B₁B₂ = B₂B₃ = B₃B_{4 .}
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, △ EBD is the required triangle, each of whose sides is$\frac{3}{4}$ the corresponding sides of ∆ABC.