Question

statement reason 1 ∠vyw ≅ ∠uyv given 2 m∠uyv + m∠vyw = 180° angles forming a linear pair sum to 180° 3 m∠uyv + m∠uyv = 180° properties of addition, subtraction, multiplication 4 m∠uyv = 90° 5 vx ⊥ uw

Explanation:

Step1: Substitute equal - angle measure

Since $\angle VYW\cong\angle UYV$, we can substitute $m\angle VYW$ with $m\angle UYV$ in the equation $m\angle UYV + m\angle VYW=180^{\circ}$ from step 2. So we get $m\angle UYV + m\angle UYV = 180^{\circ}$.

Step2: Combine like - terms

Combining the two $m\angle UYV$ terms on the left - hand side of the equation $m\angle UYV + m\angle UYV = 180^{\circ}$, we have $2m\angle UYV=180^{\circ}$.

Step3: Solve for $m\angle UYV$

Dividing both sides of the equation $2m\angle UYV = 180^{\circ}$ by 2, we get $m\angle UYV=\frac{180^{\circ}}{2}=90^{\circ}$.

Step4: Use the perpendicular definition

If the measure of the angle between two lines is $90^{\circ}$, then the two lines are perpendicular. Since $m\angle UYV = 90^{\circ}$, we can say $\overleftrightarrow{VX}\perp\overleftrightarrow{UW}$.

Answer:

1. Reason: Division property of equality (divide both sides of $2m\angle UYV = 180^{\circ}$ by 2).
2. Reason: Definition of perpendicular lines (if the angle between two lines is $90^{\circ}$, the lines are perpendicular).