Chapter 3.3, Problem 16PSB

To determine

To Prove: The congruency of $\angle W$ with respect to $\angle Y$

Explanation of Solution

Given information : In this question, we have given that $\angle 7\cong \angle 8$ and $\overline{ZY}\cong \overline{WX}$

Formula used: SAS Congruency rule.

Proof: $\angle 7\cong \angle 9$ and $\angle 8\cong \angle 10$ (Vertically Opposite Angles) Now, it is given that $\angle 7\cong \angle 8$ ,

  $\Rightarrow \angle 7\cong \angle 9$ and $\Rightarrow \angle 7\cong \angle 10$

  $\Rightarrow \angle 9\cong \angle 10$

In $\Delta ZYX$ and $\Delta XWZ$ ,

  $\overline{ZY}\cong \overline{WX}$ (Given)

  $\angle 9\cong \angle 10$ (Proved above)

  $\overline{ZX}\cong \overline{ZX}$ (Common)

  $\therefore \Delta ZYX\cong \Delta XWZ$ (BY SAS Congruency rule)

  $\therefore \angle W\cong \angle Y$ (BY CPCT)