A quadrilateral is a polygon with four sides. There are several important theorems that can help us understand the properties of quadrilaterals. Let's explore some of these theorems:

1. The Parallelogram Opposite Sides Theorem: In a parallelogram, opposite sides are congruent. For example, in parallelogram ABCD, AB is congruent to CD and BC is congruent to AD.

2. The Parallelogram Opposite Angles Theorem: In a parallelogram, opposite angles are congruent. For instance, in parallelogram ABCD, angle A is congruent to angle C and angle B is congruent to angle D.

3. The Diagonals of a Parallelogram Theorem: In a parallelogram, the diagonals bisect each other. This means that the point where the diagonals intersect divides each diagonal into two congruent segments.