Question

decide whether enough information is given to prove that $\triangle pqs \cong \triangle rqs$ using the sss congruence theorem. explain

you are given $\overline{pq} \cong \square$ and by the reflexive property of congruence, $\overline{sq} \cong \square$, but there is no way to tell whether $\overline{ps} \cong \square$. so, the triangles $\square$ be proven congruent using the sss congruence theorem.

Explanation:

Step1: Identify given congruent sides

From the diagram, $\overline{PQ} \cong \overline{RQ}$

Step2: Apply Reflexive Property

$\overline{SQ} \cong \overline{SQ}$ (shared side of both triangles)

Step3: Check missing SSS requirement

No information confirms $\overline{PS} \cong \overline{RS}$

Step4: Conclude SSS congruence status

Without all three pairs of congruent sides, SSS congruence fails.

Answer:

You are given $\overline{PQ} \cong \boldsymbol{\overline{RQ}}$ and by the Reflexive Property of Congruence, $\overline{SQ} \cong \boldsymbol{\overline{SQ}}$, but there is no way to tell whether $\overline{PS} \cong \boldsymbol{\overline{RS}}$. So, the triangles $\boldsymbol{cannot}$ be proven congruent using the SSS Congruence Theorem.