Question

complete the proof that $overleftrightarrow{vx}paralleloverleftrightarrow{su}$.
statement reason
1 $angle twxcongangle stw$ given
2 $angle rtucongangle stw$ vertical angle theorem
3 $angle twxcongangle rtu$ transitive property of congruence
4 $overleftrightarrow{vx}paralleloverleftrightarrow{su}$ angles forming a linear pair sum to $180^{circ}$ converse of corresponding angles theorem corresponding angles definition of supplementary angles vertical angle theorem

Explanation:

Step1: Recall angle - congruence facts

We are given that $\angle TWX\cong\angle STW$ and we know from the Vertical - Angle Theorem that $\angle RTU\cong\angle STW$. Then, by the Transitive Property of Congruence, we get $\angle TWX\cong\angle RTU$.

Step2: Apply parallel - line theorem

$\angle TWX$ and $\angle RTU$ are corresponding angles. According to the Converse of Corresponding Angles Theorem, if two corresponding angles are congruent, then the two lines are parallel. Since $\angle TWX\cong\angle RTU$, we can conclude that $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$.

Answer:

Converse of Corresponding Angles Theorem