Question

use the given information to complete the proof of the following theorem.
if one pair of opposite sides of a quadrilateral is both parallel and congruent, then it is a parallelogram.
by definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
use this definition in your proof.
given: $overline{wx} cong overline{yz}$
$overline{wx} \parallel overline{yz}$
prove: $wxyz$ is a parallelogram

statement reason
1 $overline{wx} cong overline{yz}$ given
2 $overline{wx} \parallel overline{yz}$ given
3 $\angle 1 \cong \angle 4$ reason?

Explanation:

Step1: Identify angle relationship

$\overline{WX} \parallel \overline{YZ}$, and $\overline{XZ}$ is a transversal. Alternate interior angles formed by parallel lines and a transversal are congruent. So $\angle 1 \cong \angle 4$.

Answer:

Alternate Interior Angles Theorem