Question

∠yxz and ∠suv are supplementary. complete the proof that $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$. statement reason 1 ∠yxz and ∠suv are supplementary given 2 m∠yxz + m∠suv = 180° definition of supplementary angles 3 m∠suv + m∠vux = 180° 4 m∠yxz + m∠suv = m∠suv + m∠vux transitive property of equality 5 m∠yxz = m∠vux 6 $overleftrightarrow{wy}paralleloverleftrightarrow{tv}$

Explanation:

Step1: Identify linear - pair angles

$\angle SUV$ and $\angle VUX$ form a linear - pair. By the definition of a linear - pair of angles, the sum of the measures of two angles in a linear - pair is $180^{\circ}$. So, the reason for statement 3 is "Definition of linear - pair of angles".

Step2: Simplify the equation

Starting from $m\angle YXZ + m\angle SUV=m\angle SUV + m\angle VUX$, we can subtract $m\angle SUV$ from both sides of the equation. According to the Subtraction Property of Equality, if $a + b=a + c$, then $b = c$. So, the reason for statement 5 is "Subtraction Property of Equality".

Step3: Use the corresponding - angles postulate

$\angle YXZ$ and $\angle VUX$ are corresponding angles. If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. So, the reason for statement 6 is "Corresponding Angles Postulate".

Answer:

1. Definition of linear - pair of angles
2. Subtraction Property of Equality
3. Corresponding Angles Postulate