Parallelogram

2016-10-18T03:55:43Z

115.112.147.254: /* Properties */Fixed typo

[[File:Parallelogram.svg|right|250px]]
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 language|Greek]] word "parallelogrammon" (''bounded by parallel lines'').<ref>{{Cite web |url= http://www.etymonline.com/index.php?search=parallelogram&searchmode=none
|title=Online Etymology Dictionary |work=etymonline.com |accessdate=10 January 2011}}</ref> [[Rectangle]]s, [[rhombus]]es, and [[Square (geometry)|squares]] are all parallelograms.

As shown in the picture on the right, because [[triangle]]s '''''ABE''''' and '''''CDE''''' are [[congruent]] (have the same shape and size),
:<math>AE = CE</math>
:<math>BE = DE.</math>

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]] <u>any one</u> of the following statements is true:<ref>Owen Byer, Felix Lazebnik and Deirdre Smeltzer, ''Methods for Euclidean Geometry'', Mathematical Association of America, 2010, pp. 51-52.</ref><ref>Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, p. 22.</ref>
*Two pairs of opposite sides are equal in length
*Two pairs of opposite angles are equal in measure
*The [[diagonal]]s bisect each other
*One pair of opposite sides are [[Parallel (geometry)|parallel]] and equal in length
*[[Adjacent angles]] are [[supplementary angles|supplementary]]
*Each diagonal divides the quadrilateral into two [[congruence (geometry)|congruent]] [[triangle]]s
*The sum of the [[Square number|square]]s 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 ==
{{Reflist}}

== Other websites ==
{{Commons|Parallelograms}}
* [http://www.elsy.at/kurse/index.php?kurs=Parallelogram+and+Rhombus&status=public Parallelogram and Rhombus - Animated course (Construction, Circumference, Area)]
*[http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/index.php Interactive Parallelogram --sides, angles and slope]

{{math-stub}}

[[Category:Polygons]]

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Parallelogram