Question

∠twx and ∠utw are supplementary. complete the proof that $overleftrightarrow{su}paralleloverleftrightarrow{vx}$. statement reason 1 ∠twx and ∠utw are supplementary given 2 $m∠twx + m∠utw = 180^{circ}$ definition of supplementary angles 3 $m∠rtu + m∠utw = 180^{circ}$ angles forming a linear pair sum to $180^{circ}$ 4 $m∠twx + m∠utw = m∠rtu + m∠utw$ transitive property of equality 5 $m∠twx = m∠rtu$ properties of addition, subtraction, multiplication, and division 6

Explanation:

Step1: Recall corresponding - angles postulate

If corresponding angles are congruent, then two lines are parallel.

Step2: Identify corresponding - angles

$\angle RTU$ and $\angle TWV$ are corresponding angles. Since $\angle TWX=\angle RTU$ (from step 5) and $\angle TWX$ and $\angle TWV$ are vertical angles (and vertical angles are congruent), $\angle RTU=\angle TWV$.

Step3: State the conclusion

$\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$ because corresponding angles $\angle RTU$ and $\angle TWV$ are congruent.

Answer:

$\overleftrightarrow{SU}\parallel\overleftrightarrow{VX}$; Corresponding angles are congruent.