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

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Given that P is a point on the bisector of an angle ΔABC, and PQ||AB.

We have to prove that ΔBPQ is isosceles

Since,

BP is bisector of ∠ABC

⇒ ∠ABP=∠PBC ......(1)

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