In the adjoining figure, AB = AC and AP = AQ. Prove that

(i) △APC ≅ △AQB

(ii) CP = BQ

(iii) ∠APC = ∠AQB.

(i) In △APC and △AQB we have,

AB = AC (Given)

AP = AQ (Given)

∠PAC = ∠QAB (Common 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.

∴ ∠APC = ∠AQB.

Hence, proved that ∠APC = ∠AQB.