Chapter 4, Problem 11RP

To determine

To Verify: $OY\perp WX.$

Explanation of Solution

Given information: $\angle 1=\angle 2$

Formula used: congruency of triangle and properties of angles.

Verification:

  $\begin{array}{l}\angle 1=\angle 2 \left(\text{given}\right) \\ \therefore \text{In}\Delta XYZ\text{and}\Delta WYZ,XY=YW\\ \text{Also},OX=OW\left(\text{Each angles to radius}\right)\text{ and }OY=OY.\\ \therefore \Delta OXY\cong \Delta OWY\left(\text{By SSS congruency}\right)\\ \therefore \angle XYZ=\angle WYZ\text{And}\text{hence}\Delta XYZ\cong \Delta WYZ.\\ \therefore \angle XYZ=\angle WYZ\\ \text{Also, by when pair axiom,}\\ \angle XYZ+\angle WYZ={180}^{\circ }.\\ \text{Hence}\angle XYZ=\angle WYZ={90}^{\circ }.\\ \because OY\perp WX.\end{array}$