In the adjoining figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ.
Prove that BQ = CP.

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Solution

$Given : A B = A C △ A B C is an isosceles triangle . A P = A Q To prove : B Q = C P Proof : A B = A C (given) A P = A Q (given) A B - A P = A C - A Q = > B P = C Q ∠ A B C = ∠ A C B (angle opposite to the equal sides are equal) = > ∠ P B C = ∠ Q C B I n △ P B C and △ Q C B : P B = Q C (proved above) ∠ P B C = ∠ Q C B (proved above) B C = B C (common) B y S A S congruence property : △ P B C ≅ △ Q C B B Q = C P (corresponding parts of the congruent triangles)$

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In the adjoining figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ. Prove that BQ = CP. Figure

In the adjoining figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ.
Prove that BQ = CP.

Figure