# Parallelogram

A parallelogram is a polygon with four sides (a quadrilateral). It has two pairs of parallel sides (sides which never meet) and four edges. 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.

## 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.

## Other websites

this is a parallelogram

a good fact paralleogram parall in itA parallelogram is a polygon with four sides (a quadrilateral). It has two pairs of parallel sides (sides which never meet) and four edges. 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 AE=CE} {\displaystyle BE=DE.} {\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.

Contents 1 Characterizations 2 Properties 3 References 4 Other websites Characterizations A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:[2][3]

Two pairs of opposite sides are equal in length Two pairs of opposite angles are equal in measure The diagonals bisect each other One pair of opposite sides are parallel and equal in length Adjacent angles are supplementary Each diagonal divides the quadrilateral into two congruent triangles The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law) It has rotational symmetry of order 2 It has two lines of symmetry Properties Opposite sides of parallelogram are parallel. Any line through the midpoint of a parallelogram bisects the area. Parallelograms are quadrilaterals. References

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

Other websites Wikimedia Commons has media related to Parallelograms. Parallelogram and Rhombus - Animated course (Construction, Circumference, Area) Interactive Parallelogram --sides, angles and slope

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this is a parallelogram a good fact paralleogram parall in it