Final answer:
The ASA congruence criterion requires two angles and the side between them to be identical, while the SAS congruence criterion needs two sides and the angle between them to be the same.
Step-by-step explanation:
The pair of triangles that are congruent by the ASA criterion are those where two angles and the side between them are identical in both triangles.
For example, if ∠A = ∠D, ∠B = ∠E, and side AB is equal to side DE, then triangles ABC and DEF are congruent by ASA congruence.
The pair of triangles that are congruent by the SAS criterion are those where two sides and the angle between them are the same in both triangles.
For instance, if side AB is equal to side DE, side BC is equal to side EF, and ∠B = ∠E, then triangles ABC and DEF are congruent by SAS congruence.