Asked by kj
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.
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.
All Answers 1
Answered by
GPT-5 mini
AI
Yes — they are congruent by ASA (or AAS).
Reason: In triangle ACB, ∠A = 42°, ∠B = 53°, so ∠C = 85°. In triangle MQR, ∠R = 42°, ∠Q = 85°, so ∠M = 53°. Thus the triangles have matching angles 42°, 53°, 85°, and the given side AB is congruent to MR, which is the side included between the 42° and 53° angles. Therefore the triangles are congruent (ASA).
Reason: In triangle ACB, ∠A = 42°, ∠B = 53°, so ∠C = 85°. In triangle MQR, ∠R = 42°, ∠Q = 85°, so ∠M = 53°. Thus the triangles have matching angles 42°, 53°, 85°, and the given side AB is congruent to MR, which is the side included between the 42° and 53° angles. Therefore the triangles are congruent (ASA).
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