Final answer:
Two triangles with one pair of congruent sides and two pairs of congruent angles would indeed be congruent by the ASA or AAS criteria; therefore, triangles with such properties cannot be non-congruent.
Step-by-step explanation:
The student's question is whether two triangles can be non-congruent but have one pair of congruent sides and two pairs of congruent angles. The answer is no; such triangles would be congruent by ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria. This means if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Similarly, if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the triangles are congruent. Both ASA and AAS are sufficient conditions for triangle congruency. Therefore, options A and B are incorrect since they suggest the triangles would not be congruent when they would be. Options C and D are trying to describe scenarios that do not negate the ASA or AAS criteria and thus are also incorrect.