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 )?
sas
sss
aas
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Explanation:

Step1: Analyze the given information

Given \(MQ = NQ\), \(Q\) 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 \(ML = PN\) (given \(\overline{LM}\cong\overline{PN}\)), \(LQ = PQ\) (since \(Q\) is the mid - point of \(\overline{LP}\)), and \(MQ = NQ\) (given).

Answer:

SSS