Asked by berlanda
Are the triangles congruent? Why or why not?
Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: Yes — option 2.
Reason: In triangle ACB the angles are 42° (A), 53° (B), and 85° (C). In triangle MQR the angles are 42° (R), 85° (Q), and therefore 53° (M). So the corresponding angles match (A↔R, B↔M, C↔Q), and the given side AB corresponds to MR and is congruent. Thus the triangles are congruent (ASA — the two angles at A and B and the included side AB correspond to the two angles at R and M and included side RM; equivalently AAS).
Reason: In triangle ACB the angles are 42° (A), 53° (B), and 85° (C). In triangle MQR the angles are 42° (R), 85° (Q), and therefore 53° (M). So the corresponding angles match (A↔R, B↔M, C↔Q), and the given side AB corresponds to MR and is congruent. Thus the triangles are congruent (ASA — the two angles at A and B and the included side AB correspond to the two angles at R and M and included side RM; equivalently AAS).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.