# Parallelogram

quadrilateral with two pairs of parallel sides

A parallelogram is a polygon with four sides (a quadrilateral). It has two pairs of parallel sides (line segments which never meet if the lines were allowed to extend beyond their end points). 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.

Parallelogram
This parallelogram is a rhomboid as it has no right angles and unequal sides.
Edges and vertices4
Symmetry groupC2, [2]+,
Areab × h (base × height);
ab sin θ (product of adjacent sides and sine of the vertex angle determined by them)
Propertiesconvex

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.

## Area formula

A parallelogram can be cut into a trapezoid and a right triangle, and be rearranged to make a rectangle. This mean the area of a parallelogram is the same with with a rectangle of the same height and base as that parallelogram:

${\displaystyle K=bh.}$

## 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.