Question

statement reason 1 $overrightarrow{uv}paralleloverrightarrow{tw}$ 2 $angle ucongangle uvx$ 3 $angle wtxcongangle uvx$ 4 $angle ucongangle twx$ 5 $angle wtxcongangle u$ 6 $angle wtxcongangle twx$

Explanation:

Step1: Given parallel lines

Given

Step2: Alternate - interior angles

If two parallel lines are cut by a transversal, alternate - interior angles are congruent. Here, $\overrightarrow{UV}\parallel\overrightarrow{TW}$ and a transversal forms $\angle U$ and $\angle UVX$.

Step3: Vertical angles are congruent

Vertical angles $\angle WTX$ and $\angle UVX$ are congruent.

Step4: Transitive property of congruence

Since $\angle U\cong\angle UVX$ and $\angle WTX\cong\angle UVX$, by the transitive property of congruence, $\angle U\cong\angle TWX$.

Step5: Symmetric property of congruence

If $\angle U\cong\angle TWX$, then by the symmetric property of congruence, $\angle WTX\cong\angle U$.

Step6: Transitive property of congruence

Since $\angle WTX\cong\angle U$ and $\angle U\cong\angle TWX$, by the transitive property of congruence, $\angle WTX\cong\angle TWX$.

Answer:

1. Given
2. Alternate - interior angles are congruent
3. Vertical angles are congruent
4. Transitive property of congruence
5. Symmetric property of congruence
6. Transitive property of congruence