Question

complete the proof that $overleftrightarrow{tv}paralleloverleftrightarrow{wy}$. statement reason 1 $angle tuxcongangle uxy$ 2 $angle suvcongangle tux$ 3 $angle uxycongangle suv$ 4 $overleftrightarrow{tv}paralleloverleftrightarrow{wy}$

Explanation:

Step1: Given

By the problem - setup, $\angle TUX\cong\angle UXY$ is given.

Step2: Vertical angles are congruent

$\angle SUV$ and $\angle TUX$ are vertical angles, so $\angle SUV\cong\angle TUX$ because vertical angles are always congruent.

Step3: Transitive property of congruence

Since $\angle TUX\cong\angle UXY$ and $\angle SUV\cong\angle TUX$, by the transitive property of congruence, $\angle UXY\cong\angle SUV$.

Step4: Corresponding - angles postulate

If two lines are cut by a transversal such that a pair of 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 have $\overleftrightarrow{TV}\parallel\overleftrightarrow{WY}$.

Answer:

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