Question

complete the proof that ∠vzw≅∠xzy. statement reason 1 m∠vzw + m∠wzx = 180° 2 m∠wzx + m∠xzy = 180° 3 m∠vzw + m∠wzx = m∠wzx + m∠xzy 4 m∠vzw = m∠xzy 5 ∠vzw≅∠xzy

Explanation:

Step1: Adjacent - supplementary angles

$\angle VZW$ and $\angle WZX$ are adjacent - supplementary angles, so $m\angle VZW + m\angle WZX=180^{\circ}$ (Definition of supplementary angles).

Step2: Adjacent - supplementary angles

$\angle WZX$ and $\angle XZY$ are adjacent - supplementary angles, so $m\angle WZX + m\angle XZY = 180^{\circ}$ (Definition of supplementary angles).

Step3: Substitution property

Since $m\angle VZW + m\angle WZX = 180^{\circ}$ and $m\angle WZX + m\angle XZY = 180^{\circ}$, we can substitute to get $m\angle VZW + m\angle WZX=m\angle WZX + m\angle XZY$.

Step4: Subtraction property of equality

Subtract $m\angle WZX$ from both sides of the equation $m\angle VZW + m\angle WZX=m\angle WZX + m\angle XZY$. We get $m\angle VZW=m\angle XZY$.

Step5: Definition of congruent angles

If $m\angle VZW=m\angle XZY$, then $\angle VZW\cong\angle XZY$ (Definition of congruent angles).

Answer:

1. Definition of supplementary angles
2. Definition of supplementary angles
3. Substitution property
4. Subtraction property of equality
5. Definition of congruent angles