Question

Construct an equilateral triangle with each side 5 cm. Then construct another triangle whose sides are 2/3 times the corresponding sides of ∆ABC.

Answer 1

Steps of Construction

Step 1. Draw a line segment BC = 5 cm.

Step 2. With B as centre and radius 5 cm, draw an arc.

Step 3. With C as centre and radius 5 cm, draw an arc cutting the previous arc at A.

Step 4. Join AB and AC. Thus, ∆ABC is the required equilateral triangle.

Step 5. Below BC, draw an acute angle ∠CBX.

Step 6. Along BX, mark three points B₁, B₂ and B₃ such that BB₁ = B₁B₂ = B₂B₃.

Step 7. Join B₃C.

Step 8. From B₂, draw B₂C' || B₃C meeting BC at C'.

Step 9. From C', draw A'C' || AC meeting AB in A'.



Here, ∆A'BC' is the required triangle, each of whose sides are $\frac{2}{3}$ times the corresponding sides of ∆ABC.