Parallelogram - Definition and Overview

A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a polygon, and more specifically a quadrilateral. Special cases of a parallelogram are the rhombus, in which all four sides are of equal length, the rectangle, in which the two sets of opposing, parallel sides are perpendicular to each other, and the square, in which all four sides are of equal length and the two sets of opposing, parallel sides are perpendicular to each other. In any parallelogram, the diagonals bisect each other, i.e, they cut each other in half.

The parallelogram law distinguishes Hilbert spaces from other Banach spaces.

It is possible to create a tessellation with any parallelogram.

The three-dimensional counterpart of a parallelogram is a parallelepiped.

See also

• parallelogram of force
• synthetic geometry

External links

• Area of Parallelogram (http://www.cut-the-knot.org/Curriculum/Geometry/AreaOfParallelogram.shtml)
• Equilateral Triangles On Sides of a Parallelogram (http://www.cut-the-knot.org/Curriculum/Geometry/EquiTriOnPara.shtml)
• Varignon Parallelogram (http://www.cut-the-knot.org/Curriculum/Geometry/Varignon.shtml)
• Wittenbauer's Parallelogram (http://www.cut-the-knot.org/Curriculum/Geometry/Wittenbauer.shtml)
• Varignon and Wittenbauer Parallelograms (http://agutie.homestead.com/files/VarigWitten.htm) by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Van Aubel's theorem (http://agutie.homestead.com/files/vanaubel.html) Quadrilateral with four squares by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Parallelogram with five squares (http://agutie.homestead.com/files/parallelogram_squares.htm) by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Mathworld: Parallelogram (http://mathworld.wolfram.com/Parallelogram.html)