Question

∠vzw ≅ ∠wzx. complete the proof that \overleftrightarrow{wy} ⊥ \overleftrightarrow{vx}.

statement
1 ∠vzw ≅ ∠wzx
2 m∠vzw + m∠wzx = 180°
3 m∠vzw + m∠vzw = 180°
4 m∠vzw = 90°
5 \overleftrightarrow{wy} ⊥ \overleftrightarrow{vx}

reason
given
angles forming a linear pair sum to 180°
substitution

definition of perpendicular lines

Explanation:

Step1: Combine like terms

$$m\angle VZW + m\angle VZW=2m\angle VZW$$
So, $2m\angle VZW = 180^{\circ}$

Step2: Solve for $m\angle VZW$

Divide both sides of the equation $2m\angle VZW = 180^{\circ}$ by 2.
$$m\angle VZW=\frac{180^{\circ}}{2}$$

Answer:

Division property of equality (or simplification of the equation \(2m\angle VZW = 180^{\circ}\) by dividing both sides by 2)