Question

given: mq = nq; q is the midpoint of lp; lm ≅ pn which congruence theorem can be used to prove △mlq ≅ △npq? aas sss asa sas

Explanation:

Step1: Analyze the given information

We know that \(MQ = NQ\), \(Q\) is the mid - point of \(\overline{LP}\) (so \(LQ=PQ\)), and \(\overline{LM}\cong\overline{PN}\).

Step2: Recall the SSS congruence theorem

The SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
In \(\triangle MLQ\) and \(\triangle NPQ\), we have \(LM = PN\) (given), \(LQ = PQ\) (since \(Q\) is the mid - point of \(LP\)), and \(MQ = NQ\) (given).

Answer:

SSS