Question

complete the proof that $\angle v \cong \angle y$.

	statement	reason
2	$\overline{xy} \parallel \overline{wz}$	given
3	$\overline{wx} \parallel \overline{vy}$	given
4	$\overline{wz} \cong \overline{xy}$	parallelograms have congruent opposite sides
5	$\overline{vw} \cong \overline{wz}$	transitive property of congruence
6	$\angle vzw \cong \angle v$	isosceles triangle theorem
7	$\angle vzw \cong \angle y$
8	$\angle v \cong \angle y$	transitive property of congruence

Explanation:

Step1: Identify parallel lines

$\overline{XY} \parallel \overline{WZ}$ and $\overline{WX} \parallel \overline{YV}$ (Given)

Step2: Recognize corresponding angles

$\angle VZW$ and $\angle Y$ are corresponding angles formed by transversal $\overline{YV}$ cutting parallel lines $\overline{XY}$ and $\overline{WZ}$.

Step3: Apply corresponding angles postulate

Corresponding angles from parallel lines are congruent, so $\angle VZW \cong \angle Y$.

Answer:

Corresponding Angles Postulate