Question

decide whether enough information is given to prove that ( \triangle pqscong\triangle rqs ) using the sss congruence theorem. explain.
you are given ( overline{pq}cong ) and by the reflexive property of congruence, ( overline{sq}cong ), but there is no way to tell whether ( overline{ps}cong ). so, the triangles be proven congruent using the sss congruence theorem.

Explanation:

Step1: Recall SSS Congruence Theorem

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.

Step2: Analyze given information

We are given \( \overline{PQ}\cong\overline{RQ}\) (from the markings on the sides of the triangles, assume \(PQ\) and \(RQ\) are corresponding sides). By the Reflexive Property of Congruence, \( \overline{SQ}\cong\overline{SQ}\) (common side). But there is no information given about the congruence of \( \overline{PS}\) and \( \overline{RS}\) (the third pair of sides for triangles \( \triangle PQS\) and \( \triangle RQS\)).

Answer:

\(\overline{RQ}\), \(\overline{SQ}\), \(\overline{RS}\), cannot