Question

Construct ∆ABC in which BC = 5.4 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 = 5.4 cm.
Step 2: Draw an angle of 60° at B, so that $\angle$XBC = 60°.
Step 3: With centre B and radius 4.5 cm, draw an arc intersecting XB at A.
Step 4: Join AC
Thus, ΔABC is the required triangle.
Step 5: Draw a line BY below BC.
Step 6: Cut off 4 equal distances from B, such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.
Step 7: Join CB₄
Step 8: Draw C'B₃ parallel to CB₄.
Step 9: Draw C'A' parallel to CA through C' intersecting BA produced to A'.
Thus, ΔA'BC' is the required similar triangle.