Question

Need help to complete the proof.

Y is the midpoint of UW. Prove △VWY ≅ △XUY. Arrange the following reasons to complete the proof.

Reasons: Given, Given, Definition of midpoint, ASA, Vertical Angle Theorem

Answer 1

To prove that triangles VWY and XUY are congruent, one would use the Definition of Midpoint, the given data that VW equals UX, the Vertical Angle Theorem, and the ASA congruence criterion, which states that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Step-by-step explanation:

The proof that triangles △VWY and △XUY are congruent can be organized by arranging the given reasons in a logical sequence:

1. Y is the midpoint of UW - Definition of midpoint.
2. VW equals UX - Given (this information would typically be provided in the problem).
3. ∠WYV equals ∠UYX - Vertical Angle Theorem.
4. VY equals UY - Since Y is the midpoint of UW, VY equals UY by the Definition of Midpoint, which implies that segments VY and UY are congruent.
5. △VWY ≅ △XUY - ASA postulate (Angle-Side-Angle congruence criterion), because two angles and the included side are congruent.

Answer 2

Here is the arranged proof:

Given: Y is the midpoint of UW.
Given: ∠VWY ≅ ∠UXY (Vertical Angle Theorem)
Definition of midpoint: Y is equidistant from U and W.
ASA: △VWY ≅ △XUY (By ASA, since Y is equidistant from U and W, and ∠VWY ≅ ∠UXY)

Therefore, △VWY ≅ △XUY is proved.