Converse Isosceles Trapezoid Base Angles Theorem

Consider an auxiliary line that passes through $C$ and is parallel to $\overline{AD}.$ Let $E$ be the intersection point of this line and $\overline{AB}.$

Applying the Parallelogram Opposite Sides Theorem, it can be concluded that $AECD$ is a parallelogram. Consequently, the opposite sides are congruent. Additionally, $\angle BEC$ and $\angle A$ are congruent because of the Corresponding Angles Theorem. Since $\angle A$ and $\angle B$ are also congruent angles, by the Transitive Property of Congruence, $\angle BEC$ is congruent to $\angle B.$ Therefore, $\angle BEC$ can be marked using one angle marker.

By the Converse Isosceles Triangle Theorem, $△BEC$ is isosceles. Therefore, $\overline{EC}$ and $\overline{BC}$ are congruent. Lastly, using the Transitive Property of Congruence once again, it is obtained that $\overline{AD}\cong \overline{BC}.$ Consequently, $ABCD$ is an isosceles trapezoid.