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

ASA (Angle - Side - Angle) 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 information

We can assume we have some angles and sides partially given. We need two angles and the side between them to be congruent in the two triangles.

Step3: Check options

We need to find an option that gives an angle - side - angle combination. The option $\angle N\cong\angle M$ would help in creating an ASA - like situation if we already have the appropriate side and other angle congruences in place.

Answer:

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