In the diagram below riangle PRS and riangle QRS. IF riangle PRS ||| riangle QRS. Prove that PS2 = PR imes PQ.

Let's analyze the information provided in the diagram and the question.

The question states: "In the diagram below $\triangle PRS$ and $\triangle QRS$. IF $\triangle PRS ||| \triangle QRS$. Prove that $PS^2 = PR \times PQ$."

However, the similarity statement "$\triangle PRS ||| \triangle QRS$" (meaning $\triangle PRS \sim \triangle QRS$) is inconsistent with the diagram and the required proof. If $\triangle PRS \sim \triangle QRS$, then $\angle PRS = \angle QRS$, which would imply $