Question

complete the proof that $overleftrightarrow{su}paralleloverleftrightarrow{vx}$. statement reason 1 $angle rtscongangle xwy$ given 2 $angle rtscongangle utw$ 3 $angle xwycongangle utw$ 4 $overleftrightarrow{su}paralleloverleftrightarrow{vx}$ converse of corresponding angles theorem

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since $\angle RTS$ and $\angle UTW$ are vertical angles, $\angle RTS\cong\angle UTW$.

Step2: Use transitive property

Given $\angle RTS\cong\angle XWY$ and $\angle RTS\cong\angle UTW$, by the transitive property of congruence, if $a = b$ and $a = c$, then $b = c$. So $\angle XWY\cong\angle UTW$.

Step3: Apply converse of corresponding - angles theorem

$\angle XWY$ and $\angle UTW$ are corresponding angles. According to the converse of the corresponding - angles theorem, if two corresponding angles are congruent, then the two lines are parallel. So $\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$.

Answer:

1. Reason: Vertical angles are congruent.
2. Reason: Transitive property of congruence.