Question

the triangles below have congruent side and angle marks. are the triangles congruent? if so, write a congruence statement and explain how you know they are congruent. justify your answer with the appropriate theorem.

Explanation:

Step1: Identify corresponding parts

In \(\triangle RLN\) and \(\triangle CAB\), \(RL = CA\) (marked as equal), \(\angle L=\angle A\) (marked as equal), \(LN = AB\) (marked as equal).

Step2: Apply congruence theorem

By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

Yes, the triangles are congruent. The congruence statement is \(\triangle RLN\cong\triangle CAB\) by the SAS (Side - Angle - Side) congruence theorem.