Perpendicular Bisector 7E65A1

1. **State the problem:** Given that \overline{WZ} is the perpendicular bisector of \overline{VY}, we need to determine which angle congruence conclusion is correct. 2. **Recall the definition of a perpendicular bisector:** A perpendicular bisector of a segment is a line that is perpendicular to the segment and divides it into two equal parts at its midpoint. 3. **Apply the properties:** Since \overline{WZ} is the perpendicular bisector of \overline{VY}, point Z is the midpoint of \overline{VY}, so \overline{VZ} \cong \overline{ZY}. 4. **Use the perpendicular property:** \overline{WZ} is perpendicular to \overline{VY}, so \angle WZV and \angle WZY are right angles and congruent. 5. **Consider triangles \triangle VWZ and \triangle YWZ:** - \overline{VZ} \cong \overline{ZY} (Z is midpoint) - \overline{WZ} is common side - \angle WZV \cong \angle WZY (right angles) 6. **By SAS (Side-Angle-Side) congruence, \triangle VWZ \cong \triangle YWZ.** 7. **Corresponding parts of congruent triangles are congruent (CPCTC), so:** $$\angle VWZ \cong \angle YWZ$$ **Final answer:** \boxed{\angle VWZ \cong \angle YWZ}