Chapter 10.6, Problem 1PSA

To determine

Give the explanation for the given proof.

Explanation of Solution

Given:

The given diagram is

  

$X$ is the midpoint of the arc $WY$ . Show that $\overline{ZX}$ bisects $\angle WZY$ .

Calculation:

Use the definition of midpoint. If $X$ is the midpoint of the arc $WY$ , then $\text{arc }WX\cong \text{arc }XY$ .

If the arcs are congruent, then the both the chords and angles are congruent.

  $\angle YZX\cong \angle WZX$

From the above results, $\overline{ZX}$ divides the angle into two congruent angles.

Hence $\overline{ZX}$ bisects $\angle WZY$ .