Theorems About Parallelograms
Rule

Converse Parallelogram Opposite Angles Theorem

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
A parallelogram with congruent opposite angles

Based on the above diagram, the following statement holds true.

Proof

Assume that is a quadrilateral with opposite congruent angles. It should be noted that congruent angles have the same measure. Then, let be the measure of and and be the measure of and

By the Polygon Interior Angles Theorem, the sum of the interior angles of a quadrilateral is With this information, a relation can be found between the consecutive interior angles of
Simplify
Since the consecutive interior angles of are supplementary. Therefore, by the Converse Consecutive Interior Angles Theorem, it can be concluded that opposite sides of are parallel.
A polygon ABCD with one movable vertex
Consequently, by the definition of a parallelogram, is a parallelogram.

Completed Proof

Proof:
Proof of the theorem
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