Question

complete the proof that ∠xwz ≅ ∠ywz.
statement\treason

1. ∠ywz ≅ ∠xyw\tgiven
2. (overline{wx}paralleloverline{vy})\tgiven
3. ∠ywz ≅ ∠wxy\t
4. ∠xwz ≅ ∠wxy\t
5. ∠ywz ≅ ∠wxy\ttransitive property of congruence
6. ∠xwz ≅ ∠ywz\t

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since $\angle VYZ$ and $\angle WXY$ are vertical angles, $\angle VYZ\cong\angle WXY$ (Vertical - Angles Theorem).

Step2: Use given congruence

We are given $\angle VYZ\cong\angle XWZ$.

Step3: Apply transitive property

If $\angle VYZ\cong\angle WXY$ and $\angle VYZ\cong\angle XWZ$, by the Transitive Property of Congruence, $\angle XWZ\cong\angle WXY$.

Answer:

1. Vertical - Angles Theorem; 4. Given; 6. Transitive Property of Congruence