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: Use the mid - point property

Since \(Q\) is the mid - point of \(\overline{LP}\), we have \(LQ = PQ\) (by the definition of a mid - point: a mid - point divides a line segment into two equal parts).

Step2: List the side - side - side (SSS) congruence condition

We are given \(MQ = NQ\), \(LM\cong PN\), and from Step 1 \(LQ = PQ\).
The SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
For \(\triangle MLQ\) and \(\triangle NPQ\), we have:

• \(ML = PN\) (given)
• \(LQ = PQ\) (from the mid - point property)
• \(MQ = NQ\) (given)

Answer:

SSS