Chapter 12, Problem 8CT

To determine

To write: The plan to prove that $\angle 1\cong \angle 2$ .

Answer to Problem 8CT

It is proved that $\angle 1\cong \angle 2$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

First by SSS Congruence Theorem to prove $\Delta VSX\cong \Delta ZSX$ .

By Vertical Angles Theorem $\angle VSR\cong \angle TSZ$ then by SAS Congruence Theorem to prove $\Delta VSR\cong \Delta TSZ$ .

Since the corresponding parts of congruent triangles are congruent. So $\angle VRS\cong \angle ZTS$ .

Therefore, it is proved that $\angle 1\cong \angle 2$ .