Look at the diagram below.If PQS RQS, then PS = RS.A.TrueB.FalseSUBMITarrow_backPREVIOUS

To analyze the statement "If $\triangle PQS \cong \triangle RQS$, then $PS = RS$," we proceed as follows:

1. Break Down the Problem

   • We need to determine if the congruence of triangles $PQS$ and $RQS$ implies that $PS$ is equal to $RS$.

2. Relevant Concepts

   • Congruent Triangles: Two triangles are congruent if all corresponding sides and angles are equal.
   • If $\triangle PQS \cong \triangle RQS$, by the definition of congruence, the corresponding sides and angles are equal:
     • $PQ = RQ$
     • $QS = QS$ (common side)
     • $PS = RS$ (corresponding sides)

3. Analysis and Detail

   • Since the triangles are congruent, we can conclude that:
     • $PS$ corresponds to $RS$ in the triangles $PQS$ and $RQS$.
     • Therefore, by the property of congruent triangles, $PS$ must equal $RS$.

4. Verify and Summarize

   • The assertion is consistent with the definition of congruency. Since all corresponding sides match under congruence, $PS = RS$ is indeed true.

Final Answer

The statement is A. True.