Question

complete the proof that ( overleftrightarrow{tv} parallel overleftrightarrow{wy} ).

Explanation:

Step1: Identify reason for Statement 1

$\angle UXY$ and $\angle TUX$ are vertical angles, so they are congruent.

Step2: Identify reason for Statement 2

$\angle SUV$ and $\angle TUX$ are vertical angles, so they are congruent.

Step3: Identify reason for Statement 3

By transitive property of congruence (from Statements 1 and 2).

Step4: Identify reason for Statement 4

$\angle UXY \cong \angle SUV$ are corresponding angles, so lines are parallel by Converse of Corresponding Angles Theorem.

Answer:

1. Vertical Angles Theorem
2. Vertical Angles Theorem
3. Transitive Property of Congruence
4. Converse of Corresponding Angles Theorem