Question

∠vyw≅∠uyv. complete the proof that $overleftrightarrow{vx}perpoverleftrightarrow{uw}$.
statement reason
1 ∠vyw≅∠uyv
2 $mangle uyv + mangle vyw=180^{circ}$
3 $mangle uyv + mangle uyv = 180^{circ}$
4 $mangle uyv = 90^{circ}$
5 $overleftrightarrow{vx}perpoverleftrightarrow{uw}$

Explanation:

Step1: Given information

Given $\angle VYW\cong\angle UYV$

Step2: Linear - pair postulate

$\angle UYV$ and $\angle VYW$ form a linear - pair, so $m\angle UYV + m\angle VYW=180^{\circ}$

Step3: Substitution property

Since $\angle VYW\cong\angle UYV$, we substitute $m\angle VYW$ with $m\angle UYV$, getting $m\angle UYV + m\angle UYV = 180^{\circ}$

Step4: Solve the equation

Combining like - terms gives $2m\angle UYV=180^{\circ}$, then dividing both sides by 2, we have $m\angle UYV = 90^{\circ}$

Step5: Definition of perpendicular lines

If the measure of the angle formed by two lines is $90^{\circ}$, the two lines are perpendicular. So $\overleftrightarrow{VX}\perp\overleftrightarrow{UW}$

Answer:

1. Given
2. Linear - pair postulate
3. Substitution property
4. Simplification (or solving the equation $2m\angle UYV = 180^{\circ}$)
5. Definition of perpendicular lines