Question

complete the proof that ∠twx≅∠stw.
statement
1 (overleftrightarrow{su}paralleloverleftrightarrow{vx})
2 ∠twx≅∠rtu
3 ∠rtu≅∠stw
4 ∠twx≅∠stw
reason

Explanation:

Step1: Given parallel lines

Given that $\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$.

Step2: Corresponding - angles postulate

Since $\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$, $\angle TWX\cong\angle RTU$ because corresponding angles formed by parallel lines and a transversal are congruent.

Step3: Vertical - angles theorem

$\angle RTU\cong\angle STW$ because vertical angles are congruent.

Step4: Transitive property of congruence

Since $\angle TWX\cong\angle RTU$ and $\angle RTU\cong\angle STW$, by the transitive property of congruence, $\angle TWX\cong\angle STW$.

Answer:

1. Given
2. Corresponding - angles postulate
3. Vertical - angles theorem
4. Transitive property of congruence