Question

determining triangle congruence
triangles abc and def have two congruent, corresponding angles. can it be concluded that triangle abc is congruent to triangle def?
options:
no, it is necessary to know that all corresponding angles are congruent.
yes, since there are two congruent, corresponding angles.
no, it is necessary to know that a set of corresponding sides is congruent.
no, it is not possible for the triangles to be congruent.

Explanation:

To determine if two triangles are congruent, we use triangle congruence criteria (ASA, SAS, SSS, AAS, HL). Having two congruent corresponding angles is not sufficient for congruence—we need at least one pair of corresponding sides to be congruent (e.g., ASA needs a side between the angles, AAS needs a side not between, etc.). The third option correctly states that knowing a set of corresponding sides is congruent is necessary, as two angles alone (AA) only implies similarity, not congruence. The first option's "all corresponding angles" is incorrect (AA for similarity, not congruence), the second option incorrectly claims two angles are enough, and the fourth is wrong as congruence is possible with proper criteria.

Answer:

The third option (the one with "No, it is necessary to know that a set of corresponding sides is congruent.")