Question

triangles abc and def have two congruent, corresponding angles. can it be concluded that triangle abc is congruent to triangle def? no, it is not possible for the triangles to be congruent. 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.

Explanation:

Step1: Recall congruence criteria

For two triangles to be congruent, we have criteria like SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg for right - angled triangles). Just having two congruent corresponding angles (AA) is not enough.

Step2: Analyze the options

Option 1: Just saying it's not possible is too general. Option 2: Knowing all angles are congruent gives similarity, not congruence. Option 3: Two angles alone don't imply congruence. Option 4: For congruence with two angles known, we need a set of corresponding sides to be congruent (either ASA or AAS).

Answer:

No, it is necessary to know that a set of corresponding sides is congruent.