Question

Construct a ∆ABC in which AB = 5 cm, BC = 6 cm and CA = 7 cm. Construct a triangle similar to ∆ABC, such that each of its side is $\frac{5}{7}$ the corresponding sides of ∆ABC.

Answer 1

Steps of Construction :

Step 1. Draw a line segment BC = 6 cm.
Step 2. With B as centre and radius equal to 5 cm, draw an arc.
Step 3. With C as centre and radius equal to 7 cm, draw another arc, cutting the previous arc at A.
Step 4. Join AB and AC.
Thus, $△ABC\mathrm{is}\mathrm{obtained}.$
Step 5. Below BC, draw an acute $\angle CBX.$
Step 6. Along BX, mark off seven points B₁, B₂, B₃, B₄, B_5, B_6, B_7, such that B₁B₂ = B₂B₃ = B₃B_{4 =} B₄B₅ = B₅B₆ = B₆B₇.
Step 7. Join B₇C.
Step 8. From B₅, draw B₅D $\parallel$ B₇C, meeting BC at D.
Step 9. From D, draw $DE\parallel CA$, meeting AB at E.


Thus, $△EBD$ is the required triangle, each of whose sides is $\frac{5}{7}$ the corresponding sides of ∆ABC.