Question

complete the proof that $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$. statement reason 1 $angle uxycongangle tux$ given 2 $angle suvcongangle tux$ vertical angle theorem 3 4 $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$ converse of corresponding angles theorem

Explanation:

Step1: Transitive property of congruence

Since $\angle UXY\cong\angle TUX$ (given) and $\angle SUV\cong\angle TUX$ (vertical - angle theorem), by the transitive property of congruence, $\angle UXY\cong\angle SUV$.

Step2: Apply converse of corresponding - angles theorem

The converse of the corresponding - angles theorem states that if two corresponding angles are congruent, then the two lines are parallel. Since $\angle UXY$ and $\angle SUV$ are corresponding angles and $\angle UXY\cong\angle SUV$, we can conclude that $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$.

Answer:

1. $\angle UXY\cong\angle SUV$; Transitive property of congruence