Question

z is the midpoint of \\( \overline{xy} \\) and \\( \overline{xy} \perp \overline{wz} \\). complete the proof that \\( \angle x \cong \angle y \\).

Explanation:

Step1: Reason for $\overline{XZ} \cong \overline{YZ}$

Z is midpoint of $\overline{XY}$, so it divides $\overline{XY}$ into two congruent segments.
Reason: Definition of midpoint

Step2: Reason for $\overline{WZ} \cong \overline{WZ}$

The segment $\overline{WZ}$ is common to both triangles $\triangle WXZ$ and $\triangle WYZ$.
Reason: Reflexive property of congruence

Answer:

Step4 reason: Definition of midpoint
Step5 reason: Reflexive property of congruence