Question

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

Answer 1

To prove: BPQ is an isosceles triangle.

According to the question,

Since, BP is the bisector of ∠ABC,

∠1 = ∠2 … (1)

Now, PQ is parallel to BA and BP is a transversal

∠1 = ∠3 [Alternate angles] … (2)

From equations, (1) and (2),

We get

∠2 = ∠3

In $\Delta$ BPQ,

We have

∠2 = ∠3

PQ = BQ

Hence, BPQ is an isosceles triangle.