Question

complete the proof that ∠vwx≅∠uvw.
statement reason
1 ∠txu = ∠uvw given
2 vw || ux given
3 ∠vwx = ∠txu
4 ∠vwx = ∠uvw

Explanation:

Step1: Recall parallel - line property

If two parallel lines are cut by a transversal, corresponding angles are congruent. Since $\overleftrightarrow{VW}\parallel\overleftrightarrow{UX}$ (given), $\angle VWX$ and $\angle TXU$ are corresponding angles. So, $\angle VWX\cong\angle TXU$ because of the Corresponding Angles Postulate.

Step2: Use the transitive property of congruence

We know that $\angle TXU\cong\angle UVW$ (given) and $\angle VWX\cong\angle TXU$. By the Transitive Property of Congruence, if $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$. Here, $A = \angle VWX$, $B=\angle TXU$ and $C = \angle UVW$. So, $\angle VWX\cong\angle UVW$.

Answer:

1. Corresponding Angles Postulate
2. Transitive Property of Congruence