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 and options

We need to find the additional information for ASA. We already have right - angles in both triangles. We need another pair of angles and the included side between them. Looking at the options, if $\angle N\cong\angle M$, along with the right - angles and the common side (the side between the right - angle and the angle we are adding), we can use ASA. The other options are about side - side congruence or wrong angle pairs.

Answer:

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