Mathematics
In the adjoining figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that
(i) △APC ≅ △AQB
(ii) CP = BQ
(iii) ∠ACP = ∠ABQ.
Triangles
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Answer
(i) In △APC and △AQB we have,
AP = AQ (Given)
AB = AC (Given)
∠PAC = ∠QAB (Vertically opposite angles)
Hence, by SAS axiom △APC ≅ △AQB.
(ii) As, △APC ≅ △AQB.
We know that corresponding sides of congruent triangles are equal.
∴ CP = BQ.
Hence, proved that CP = BQ.
(iii) As, △APC ≅ △AQB.
We know that corresponding angles of congruent triangles are equal.
∴ ∠ACP = ∠ABQ.
Hence, proved that ∠ACP = ∠ABQ.
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Related Questions
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In the adjoining figure, AB = AC and AP = AQ. Prove that
(i) △APC ≅ △AQB
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(iii) ∠APC = ∠AQB.
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