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Question

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

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Solution



Given: BP is the bisector of ∠ABC, and BAQP

To prove: ΔBPQ is an isosceles triangle

Proof:

1=2 Given, BP is the bisector of ABCAnd, 1=3 Alternate interior angles2=3So, PQ=BQ In a triangle, sides opposite to equal sides are equal.

But these are sides of BPQ.

Hence, BPQ is an isosceles triangle.

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