In triangles ABC and PQR it is given that AB = PQ, ∠A = ∠P and ∠C = ∠R. Which criterion establishes that the two triangles are congruent?

The two equal angles are at A and C, while the equal side AB joins A and B. The side is therefore NOT the one lying between the two given angles, so ASA does not fit as stated — this is two angles and a non-included side, the AAS criterion. AAS is valid because the third angles must then agree too (∠B = ∠Q), which converts it into ASA. SAS would need a second pair of equal sides, and SSA is never a criterion.