Question

∠wxz and ∠sut are supplementary. complete the proof that (overleftrightarrow{wy}paralleloverleftrightarrow{tv}).
statement
1 ∠wxz and ∠sut are supplementary
2 (mangle wxz + mangle sut=180^{circ})
3 (mangle sut + mangle tux = 180^{circ})
4 (mangle wxz + mangle sut=mangle sut + mangle tux)
5 (mangle wxz=mangle tux)
6 (overleftrightarrow{wy}paralleloverleftrightarrow{tv})

Explanation:

Step1: Define supplementary angles

By definition, if two angles are supplementary, the sum of their measures is 180°. So, since $\angle WXZ$ and $\angle SUT$ are supplementary, $m\angle WXZ + m\angle SUT=180^{\circ}$.

Step2: Use linear - pair property

$\angle SUT$ and $\angle TUX$ form a linear - pair. A linear - pair of angles is supplementary, so $m\angle SUT + m\angle TUX = 180^{\circ}$.

Step3: Transitive property of equality

Since $m\angle WXZ + m\angle SUT=180^{\circ}$ and $m\angle SUT + m\angle TUX = 180^{\circ}$, by the transitive property of equality (if $a + b=c + b$, then $a = c$), we have $m\angle WXZ + m\angle SUT=m\angle SUT + m\angle TUX$.

Step4: Subtraction property of equality

Subtract $m\angle SUT$ from both sides of the equation $m\angle WXZ + m\angle SUT=m\angle SUT + m\angle TUX$. We get $m\angle WXZ=m\angle TUX$.

Step5: Use corresponding - angles postulate

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

Answer:

The proof is completed by using the definitions of supplementary and linear - pair angles, the transitive and subtraction properties of equality, and the corresponding - angles postulate to show that $\overleftrightarrow{WY}\parallel\overleftrightarrow{TV}$.