Question

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

Explanation:

Step1: Recall ASA requirements

ASA needs two angles and included side congruent.

Step2: Identify given angles

Right angles at Q and K (∠PQM=∠NKM=90°). Vertical angles ∠PMQ=∠NMK.

Step3: Determine needed included side

Included sides: QM (△PQM) and KM (△NKM). Need QM≅KM.

Answer:

NK ≅ MQ