Question

Complete the proof that ∠UXY≅∠TUX.

S
T
U
V
W
X
Y
Z
Statement Reason
1
WY
∥
TV
Given
2 ∠UXY≅∠SUV Corresponding Angles Postulate
3 ∠SUV≅∠TUX Vertical Angle Theorem
4 ∠UXY≅∠TUX

Answer 1

The proof demonstrates that angles ∠UXY and ∠TUX are congruent by applying the Corresponding Angles Postulate and the Vertical Angle Theorem, building on the principles of logical progression and consistent application of postulates.

Step-by-step explanation:

To complete the proof that ∠UXY ≅ ∠TUX, given that WY is parallel to TV and ∠UXY is congruent to ∠SUV, here are the steps:

1. WY∥TV - Given
2. ∠UXY ≅ ∠SUV - Corresponding Angles Postulate, since WY is parallel to TV and a transversal cuts through them, the corresponding angles are congruent.
3. ∠SUV ≅ ∠TUX - Vertical Angle Theorem, which states that opposite (vertical) angles are congruent.
4. Therefore, by the transitive property of equality, if ∠UXY ≅ ∠SUV and ∠SUV ≅ ∠TUX, it follows that ∠UXY ≅ ∠TUX.

This logical progression, similar to elements of trigonometry and physics, is built on the consistent application of postulates, ensuring that outcomes are predictable and repeatable when applied correctly.