Question

Construct a ∆ABC in which BC = 8 cm, B = 45º and C = 60º. Construct another triangle similar to ∆ABC such that its sides are of the corresponding sides of ∆ABC. [CBSE 2010, '12, '14]

Answer 1

Steps of Construction

Step 1. Draw a line segment BC = 8 cm.

Step 2. At B, draw $\angle$XBC = 45º.

Step 3. At C, draw $\angle$YCB = 60º. Suppose BX and CY intersect at A.

Thus, ∆ABC is the required triangle.

Step 4. Below BC, draw an acute angle $\angle$ZBC.

Step 5. Along BZ, mark five points Z₁, Z₂, Z₃, Z₄ and Z₅ such that BZ₁ = Z₁Z₂ = Z₂Z₃ = Z₃Z₄ = Z₄Z₅.

Step 6. Join CZ₅.

Step 7. From Z₃, draw Z₃C' || CZ₅ meeting BC at C'.

Step 8. From C', draw A'C' || AC meeting AB in A'.



Here, ∆A'BC' is the required triangle whose sides are $\frac{3}{5}$ of the corresponding sides of ∆ABC.