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),

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]