Question

complete the proof that $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$. 1. $angle suvcongangle wxz$ given 2. $angle suvcongangle tux$ angles - forming a linear pair sum to 180° 3. $angle wxzcongangle tux$ transitive property of congruence 4. $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$

Explanation:

Step1: Identify given congruent angles

Given $\angle SUV\cong\angle WXZ$.

Step2: Recall vertical - angle property

$\angle SUV\cong\angle TUX$ because vertical angles are congruent.

Step3: Apply transitive property

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

Step4: Use corresponding - angles postulate

$\angle WXZ$ and $\angle TUX$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel. So, $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$ by the corresponding - angles postulate.

Answer:

The reason for statement 4 is "Corresponding - Angles Postulate"