The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry. 
Home Analytic Geometry Quadrilateral Parallelogram and Rhombus  
See also: Quadrilateral  General Definitions, Rectangle and Square, Tangential Quadrilateral  
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Parallelogram and RhombusA parallelogram is a quadrilateral with parallel opposite sides. As a consequence of the parallel sides the opposite angles are equal: α = γ, and β = δ.
A parallelogram with equal sides (a = b) is called a rhombus, a parallelogram whose angles are all right angles is called a rectangle.
The diagonals of a parallelogram bisect each other, the diagonals of a rhombus intersect at a right angle. The diagonals and the sides of a parallelogram are related by the following equation: d_{1}^{2} + d_{2}^{2} = 2(a^{2} + b^{2}) If the sides a and b of a parallelogram are given as vectors u = AB and v = AD, then the area of the parallelogram can be calculated by the cross product of the two vectors: A = uxv


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