Question

complete the proof that $overleftrightarrow{vx}paralleloverleftrightarrow{su}$. 1. $angle twxcongangle stw$ given 2. $angle rtucongangle stw$ 3. $angle twxcongangle rtu$ 4. $overleftrightarrow{vx}paralleloverleftrightarrow{su}$

Explanation:

Step1: Transitive - property of congruence

Since $\angle TWX\cong\angle STW$ (given) and $\angle RTU\cong\angle STW$ (given), by the transitive - property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), we have $\angle TWX\cong\angle RTU$.

Step2: Corresponding - angles postulate

$\angle TWX$ and $\angle RTU$ are corresponding angles. If corresponding angles are congruent, then the two lines are parallel. So, $\overleftrightarrow{VX}\parallel\overleftrightarrow{SU}$.

Answer:

1. Reason: Vertical - angles are congruent.
2. Reason: Transitive property of congruence.
3. Reason: Corresponding angles postulate.