Question

what additional information is needed to prove that the triangles are congruent using the asa congruence theorem?
○ nl ≅ mp
○ nk ≅ mq
○ ∠n ≅ ∠m
○ ∠l ≅ ∠p

Explanation:

Step1: Recall ASA congruence theorem

The ASA (Angle - Side - Angle) congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze given options

We need to find the pair of angles that, along with the side between them, would satisfy ASA. Given the nature of the problem, we are looking for a pair of angles. Options $\overline{NL}\cong\overline{MP}$ and $\overline{NK}\cong\overline{MQ}$ are about side - side congruence which is not relevant for ASA. We need two angles and the side between them. If we have $\angle N\cong\angle M$, along with the common side and another pair of angles, we can use ASA.

Answer:

C. $\angle N\cong\angle M$