Answer:
To prove angle VWY = angle XUY using the provided statements:
1. Y is the midpoint of line segment UW (Given)
2. angle U is congruent to angle W (Vertical angles are congruent)
3. UY is congruent to WY (Definition of midpoint)
4. angle UYX is congruent to \angle VYW (Vertical angles are congruent)
5. Triangle VWY is congruent to Triangle XUY (Angle-Side-Angle congruence)
Arranging the reasons:
1. Given
2. Vertical angles are congruent
3. Definition of midpoint
4. Vertical angles are congruent
5. Angle-Side-Angle congruence
