are the triangles congruent? why or why not?\nyes, all the angles of each of the triangles are acute.\nyes…
are the triangles congruent? why or why not?\nyes, all the angles of each of the triangles are acute.\nyes, they are congruent by either asa or aas.\nno, ∠b is not congruent to ∠q.\nno, the congruent sides do not correspond.
Answer
Answer:
B. Yes, they are congruent by either ASA or AAS.
Explanation:
Step1: Find angle - C in triangle ABC
In $\triangle ABC$, using the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$), $\angle A = 42^{\circ}$ and $\angle B=53^{\circ}$, so $\angle C=180-(42 + 53)=85^{\circ}$.
Step2: Identify congruent parts
In $\triangle ABC$ and $\triangle RMQ$, $\angle A=\angle R = 42^{\circ}$, $\angle C=\angle Q = 85^{\circ}$, and there is a pair of congruent sides (the marked sides). So, by either the Angle - Side - Angle (ASA) or Angle - Angle - Side (AAS) congruence criterion, the two triangles are congruent.