Chapter 2.4, Problem 10PSB

To determine

To Prove: $\angle 1\cong \angle 3$

Explanation of Solution

Given information: $OA\perp OC,OR\perp OD$ .

  

Proof: $OA\perp OC,OR\perp OD$ (Given)

  $\therefore \angle AOC={90}^{\circ }$ And $\angle BOD={90}^{\circ }$ (by definition of perpendicular lines)

  $\begin{array}{l}\therefore \angle AOC=\angle BOD\\ \therefore \angle 1+\angle 2=\angle 2+\angle 3\\ \therefore \angle 1=\angle 3\end{array}$