Quadrilaterals are prevalent shapes in the world, and thus have been classified carefully. The four sides of quadrilaterals naturally come in pairs, with opposite sides being those that don't share a vertex. Many quadrilaterals have pairs of opposite sides with no special relationships, but then again, some do.
A parallelogram is a quadrilateral whose opposite sides are parallel. Below a few parallelograms are pictured.
A parallelogram has many interesting properties. Its opposite sides, in addition to being parallel, are congruent. The opposite angles of a parallelogram are also congruent. Consecutive angles of a parallelogram, are supplementary. Also, the diagonals of a parallelogram bisect each other. These properties are pictured below.
Parallelograms can be broken down into different categories as well. Parallelograms with four congruent sides are called rhombuses. Parallelograms with four right angles are called rectangles. And a parallelogram whose sides and angles are all congruent is a square.
A quadrilateral with only one pair of parallel sides is called a trapezoid. Here some trapezoids are pictured.
These special quadrilaterals are helpful because they can be used as estimates of real-life four-sided shapes, and their properties make calculations easy.