Question

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

Explanation:

Step1: Given information

Given

Step2: Definition of supplementary angles

Definition of supplementary angles (if two angles are supplementary, the sum of their measures is 180°)

Step3: Linear - pair postulate

$\angle SUV$ and $\angle VUX$ form a linear - pair, so the sum of their measures is 180°

Step4: Transitive property of equality

Since $m\angle UXY + m\angle VUX=180^{\circ}$ and $m\angle SUV + m\angle VUX = 180^{\circ}$, we can set them equal to each other

Step5: Subtraction property of equality

Subtract $m\angle VUX$ from both sides of the equation $m\angle UXY + m\angle VUX=m\angle SUV + m\angle VUX$

Step6: Corresponding - angles converse

$\angle UXY$ and $\angle SUV$ are corresponding angles. If corresponding angles are congruent, then the lines are parallel

Answer:

1. Given
2. Definition of supplementary angles
3. Linear - pair postulate
4. Transitive property of equality
5. Subtraction property of equality
6. Corresponding - angles converse