Question

given: mq = nq; q is the midpoint of \overline{lp}; \overline{lm} \cong \overline{pn} which congruence theorem can be used to prove \triangle mlq \cong \triangle npq? \bigcirc aas \bigcirc sss \bigcirc asa \bigcirc sas

Explanation:

Step1: Analyze given information

We know \( MQ = NQ \) (given), \( Q \) is the midpoint of \( \overline{LP} \), so \( LQ = PQ \) (definition of midpoint), and \( \overline{LM} \cong \overline{PN} \) (given).

Step2: Identify congruence theorem

In \( \triangle MLQ \) and \( \triangle NPQ \), we have three sides: \( LM = PN \), \( MQ = NQ \), and \( LQ = PQ \). 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. So we can use the SSS congruence theorem.

Answer:

B. SSS