Question

wy || tv. complete the proof that ∠vux ≅ ∠uxw.
statement\treason
1 wy || tv\tgiven
2 ∠uxw ≅ ∠sut\t
3 ∠sut ≅ ∠vux\t
4 ∠vux ≅ ∠uxw\t

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. $\angle UXW$ and $\angle SUT$ are vertical angles, so $\angle UXW\cong\angle SUT$.

Step2: Identify vertical - angle property again

$\angle SUT$ and $\angle VUX$ are vertical angles. Since vertical angles are congruent, $\angle SUT\cong\angle VUX$.

Step3: Use the transitive property of congruence

If $\angle UXW\cong\angle SUT$ and $\angle SUT\cong\angle VUX$, then by the transitive property of congruence, $\angle VUX\cong\angle UXW$.

Answer:

1. Vertical angles are congruent.
2. Vertical angles are congruent.
3. Transitive property of congruence.