Question

In Fig 6.7, ∠D = ∠E and AD/DB = AE/EC . Prove that BAC is an isosceles triangle.

Answer 1

Solution :AD/DB = AE/EC (Given)

Therefore, DE ∥ BC (Converse of Basic Proportionality Theorem)

So, ∠D = ∠B and ∠E = ∠C (Corresponding angles) (1)

But ∠D = ∠E (Given)

Therefore, ∠B = ∠C [ From (1)]

So, AB = AC (Sides opposite to equal angles)

i.e., BAC is an isosceles triangle.