Chapter 2, Problem 25RP

To determine

To Prove: The congruency of $\angle 3$ with respect to $\angle 1$

Explanation of Solution

Given information: $\overrightarrow{VY}$ bisects $\angle TVZ$

  $\overrightarrow{ZY}$ bisects $\angle TZV$

  $\angle TVZ\cong \angle TZV$

Proof: Here, $\overrightarrow{VY}$ bisects $\angle TVZ$

So, $\angle 2=\angle YVZ$

And, $\overrightarrow{ZY}$ bisects $\angle TZV$

So, $\angle 3=\angle YZV$

And, $\angle TVZ\cong \angle TZV$ (given)

So that, $TV=TZ$

And, $\angle 2=\angle 3$ (angle opposite to equal sides are equal)

And, $\angle 1=\angle 2$ (vertically opposite angles)

So that, here we find that

  $\angle 3\cong \angle 1$