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: List given congruent sides

1. $MQ = NQ$ (given)
2. $LQ = QP$ (Q is midpoint of $\overline{LP}$)
3. $\overline{LM} \cong \overline{PN}$ (given)

Step2: Match to congruence theorem

All three pairs of corresponding sides of $\triangle MLQ$ and $\triangle NPQ$ are congruent, which fits the SSS (Side-Side-Side) congruence criterion.

Answer:

C. SSS