Chapter 10.1, Problem 2PSA

To determine

To Prove: That $\angle S\cong \angle T$ in the given figure

Explanation of Solution

Given information:

We know that in the figure $\odot \text{Q,}\overline{\text{PR}}\perp \overline{ST}$

  

Proof :

  $\begin{array}{l}\overline{PR}\perp \overline{ST}\\ \overline{PR}\text{ bisects }\overline{\text{ST}}\\ \text{If a point is on the perpendicular bisector of a segment,}\\ \text{then it is equidistant from the end points}\text{.}\\ \overline{\text{PS}}\cong \overline{PT}\\ Now,RS=RTandPS\cong PT\\ \text{And PR is common in, two triangles,}\\ \text{RSP and RTP are equilateral}\text{.}\\ \text{Therefore, }\angle \text{S}\cong \angle \text{T are equal}\text{.}\end{array}$