Parallelogram

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Parallelogram.svg

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),

AE = CE
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[change | change source]

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

Properties[change | change source]

  1. Opposite sides of parallelogram are parallel.
  2. Any line through the midpoint of a parallelogram bisects the area.
  3. Parallelogram is a quadrilateral.

References[change | change source]

  1. "Online Etymology Dictionary". etymonline.com. http://www.etymonline.com/index.php?search=parallelogram&searchmode=none. 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[change | change source]