Chapter 3.7, Problem 17PSB

To determine

To prove : $\overrightarrow{XA}$ bisects the $\angle BXZ$ .

Explanation of Solution

Given information : The following information has been given

YZ is the base of an isosceles triangle

  $\angle 2\cong \angle Z$

  $\angle 1\cong \angle Y$

Formula used : The angles on the base of an isosceles triangle are congruent

Proof : We know that YZ is the base of an isosceles triangle. Thus, we can say that

  $\angle Z\cong \angle Y$

But, we know that

  $\angle 2\cong \angle Z$ and $\angle 1\cong \angle Y$

Thus, we can conclude that

  $\angle 1\cong \angle 2$

Now, we know that

  $\angle 1+\angle 2=\angle BXZ$

Thus, from the last two equations we can say that $\overrightarrow{XA}$ bisects the $\angle BXZ$

Hence, required bisection has been proved