Chapter 10.1, Problem 7PSA

To determine

To Prove: That $\odot \text{P}\cong \odot Q$ in the given figure

Explanation of Solution

Given information:

PQRS is isosceles trapezoid with $\overleftrightarrow{SR}\left|\right|\overleftrightarrow{PQ}.$

  

Proof :

  $\begin{array}{l}\text{Since PQ || SR}\\ \text{Extending PS and RQ to O}\text{.}\\ \frac{\text{PS}}{\text{OP}}=\frac{QR}{OQ}\Rightarrow \frac{OP}{OQ}=\frac{PS}{QR}=1\\ OP=OQ\text{ and }PS=QR\\ [\odot P\cong \odot Q]\end{array}$