Question

you are given two triangles and the information that the three pairs of corresponding angles are congruent. what other information would guarantee that the triangles are congruent? a the triangles are right. b all corresponding sides are proportional. c one pair of corresponding sides is proportional. d one pair of corresponding sides has the same measure.

Explanation:

To determine which information guarantees triangle congruence when corresponding angles are congruent:

• Option A: Right triangles with congruent angles could be similar (e.g., 30 - 60 - 90 triangles of different sizes), not necessarily congruent.
• Option B: Proportional sides mean similarity, not congruence (sides can be scaled).
• Option C: One proportional side with congruent angles means similarity, not congruence.
• Option D: If one pair of corresponding sides has the same measure (congruent) and all angles are congruent, by ASA (Angle - Side - Angle) or AAS (Angle - Angle - Side) congruence criteria, the triangles are congruent.

Answer:

D. One pair of corresponding sides has the same measure.