Question

state what additional information is required in order to know that the triangles are congruent for the reason given. aas a) $overline{sr}congoverline{ml}$ b) $overline{qs}congoverline{km}$ c) $angle scongangle m$ d) $angle rcongangle l$

Explanation:

Step1: Recall AAS congruence criterion

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Step2: Analyze given information

We need to identify the non - included side and two angles for the AAS criterion. Looking at the triangles, we already have one pair of angles marked as congruent. We need another pair of angles and a non - included side. Among the options, for AAS, we need to have another pair of angles congruent.

Step3: Evaluate options

Option A and B are about side - side congruence which is not relevant for AAS. Option C gives us another pair of angles $\angle S\cong\angle M$. This along with the already marked pair of angles and a non - included side (which is yet to be considered in the context of the two angles) will satisfy AAS. Option D gives an angle that is not in the correct position for the AAS criterion with the given marked angle.

Answer:

C. $\angle S\cong\angle M$