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 from the figure that we already have one pair of right - angles (the right - angles at K and Q) and one pair of congruent sides (the marked congruent sides). We need another pair of angles where the side between them is the congruent side we already know.

Step3: Determine the needed angle

The angles that share the common side with the right - angle and the marked congruent side are ∠N and ∠M. So we need ∠N≅∠M.

Answer:

∠N≅∠M