Final answer:
To prove that ZX is the perpendicular bisector of side WY, we can use a two-column proof. We need to show that ZX bisects WY and is perpendicular to it. By using the given information and the properties of angles and equality, we can demonstrate that ZX meets both of these criteria.
Step-by-step explanation:
To prove that ZX is the perpendicular bisector of side WY, we need to show that ZX bisects WY and is perpendicular to it. Here is a two-column proof to demonstrate this:
Statement Reason
1. ZX bisects WY Given
2. ZW = WY Definition of a perpendicular bisector
3. ZX = ZX Reflexive property of equality
4. ∠XZW = ∠YWZ Vertical angles are congruent
5. ZX bisects WY and is perpendicular to it Definition of a perpendicular bisector
Therefore, ZX is the perpendicular bisector of side WY.