Question

$\overleftrightarrow{wz} \parallel \overleftrightarrow{xy}$ and $\angle wxy \cong \angle vzw$. complete the proof that $\angle wxy \cong \angle xyz$.

Explanation:

Step1: Alternate interior angles

Since \(\overleftrightarrow{WZ}\parallel\overleftrightarrow{XY}\), when a transversal \(VY\) intersects them, by the alternate - interior angles theorem, \(\angle XYZ\cong\angle VZW\).

Step2: Transitive property of congruence

We know that \(\angle WXY\cong\angle VZW\) (given) and \(\angle XYZ\cong\angle VZW\) (from step 1). By the transitive property of congruence (if \(a = b\) and \(b = c\), then \(a = c\)), \(\angle WXY\cong\angle XYZ\).

Answer:

1. Alternate - interior angles theorem; 4. Transitive property of congruence.