Chapter 3, Problem 9CR

To determine

To prove : The congruency of $\angle S$ with respect to $\angle QRS$ .

Explanation of Solution

Given information : Here, we have given that $\overline{PS}\perp \overline{SR}$ , $\angle QRP$ is complementary to $\angle PRS$ .

Formula: Complementary angles are the angles whose sum is $90°$ .

Proof: As, $\overline{PS}\perp \overline{SR}$ ,

  $\Rightarrow \angle PSR=90°$

As, $\angle QRP$ is complementary to $\angle PRS$ .

  $\begin{array}{l}\Rightarrow \angle QRP+\angle PRS=90°\\ \Rightarrow \angle QRS=90°\end{array}$

  $\therefore \angle S\cong \angle QRS$