Question

q is the midpoint of \\( \overline { p r } \\). complete the proof that \\( \delta p q s \cong \delta r q t \\).

Explanation:

Step1: Recall the SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the sides of the triangles

In \(\triangle PQS\) and \(\triangle RQT\), we have \(\overline{PQ}\cong\overline{RQ}\) (from the definition of mid - point, since \(Q\) is the mid - point of \(\overline{PR}\)), \(\overline{PS}\cong\overline{RT}\) (given), and \(\overline{QS}\cong\overline{QT}\) (given).

Answer:

\(\triangle PQS\cong\triangle RQT\) by the SSS (Side - Side - Side) congruence criterion.