# Parallelogram

A parallelogram is a polygon with four sides (a quadrilateral). It has two pairs of parallel sides (sides which never meet). The opposite sides of a parallelogram have the same length (they are equally long). The word "parallelogram" comes from the Greek word "parallelogrammon" (bounded by parallel lines).[1] Rectangles, rhombuses, and squares are all parallelograms.

As shown in the picture on the right, because triangles ABE and CDE are congruent (have the same shape and size),

${\displaystyle AE=CE}$
${\displaystyle BE=DE.}$

In all Parallelogram's opposite angles are equal to each other. Angles which are not opposite in the Parallelogram will add up to 180 degrees.

## Characterizations

A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:[2][3]

## Properties

1. Opposite sides of parallelogram are parallel.
2. Any line through the midpoint of a parallelogram bisects the area.
3. Parallelograms are quadrilaterals.

## References

1. "Online Etymology Dictionary". etymonline.com. Retrieved 10 January 2011.
2. Owen Byer, Felix Lazebnik and Deirdre Smeltzer, Methods for Euclidean Geometry, Mathematical Association of America, 2010, pp. 51-52.
3. Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, p. 22.