Chapter 14, Problem 2PE

To determine

To prove: $\angle PSO\cong \angle QRO$

Explanation of Solution

Given information:

  $\overline{PR}\perp \overline{QS},\overline{PS}\cong \overline{QR},\overline{OS}\cong \overline{OR}$ of the given figure.

  

Calculation:

From $\Delta PSQ$ and $\Delta QRP$ ,

  $\begin{array}{l}PQ=PQ\text{ (Common side)}\\ \angle SPQ=\angle PQR\text{ (Corrsponding angle of the side }PQ\text{)}\\ PS=QR\text{ (Two congruent sides)}\end{array}$

Therefore by side-angle-side formula $\Delta PSQ$ and $\Delta QRP$ are congruent. Which follows angles of congruent triangles are equal that is $\angle PSO\cong \angle QRO$ .

Hence proved.