Quadrilaterals with Congruent Opposite Angles are Parallelograms

In last week’s post, we have learned that quadrilaterals with congruent opposite sides are parallelograms. In this post, we show a related theorem. That is, quadrilaterals whose opposite angles are congruent are parallelograms.

quadrilateral abcd

In the figure above, $latex ABCD$ is a quadrilateral where $latex \angle A$ and $latex \angle C$ are congruent and $latex \angle D$ and $latex \angle B$ are congruent. In proving the theorem, we need to show that the opposite sides of $latex ABCD$ are parallel. That is $latex \overline {AB}$ is parallel to $latex \overline{CD}$ and $latex \overline {AD}$ is parallel to $latex \overline {BC}$. Continue reading