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A parallelogram.

In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are congruent. The three-dimensional counterpart of a parallelogram is a parallelepiped.

• The two parallel sides are of equal length.
• The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
• The area is also equal to the magnitude of the vector cross product of two adjacent sides.
• The diagonals of a parallelogram bisect each other.
• It is possible to create a tessellation of a plane with any parallelogram.
• The parallelogram is a special case of the trapezoid.
• The rectangle is a special case of the parallelogram.
• The rhombus is a special case of the parallelogram.

In a vector space, addition of vectors is usually defined using the parallelogram law. The parallelogram law distinguishes Hilbert spaces from other Banach spaces.

To prove that the diagonals of a parallelogram bisect each other, first note a few pairs of equivalent angles:

Since they are angles that a transversal makes with parallel lines AB and DC.

Also, since they are a pair of vertical angles.

Therefore, since they have the same angles.

From this similarity, we have the ratios

Since AB = DC, we have

.

Therefore,

AE = CE

BE = DE

E bisects the diagonals AC and BD.

• Fundamental parallelogram
• Parallelogram of force
• Rhombus
• Synthetic geometry
• Gnomon (figure)

• Parallelogram and Rhombus - Animated course (Construction, Circumference, Area)
• Eric W. Weisstein, Parallelogram at MathWorld.
• Interactive Parallelogram --sides, angles and slope
• Area of Parallelogram at cut-the-knot
• National Parallogram Dealers WebsiteNational Parallelogram Dealers Association
• Equilateral Triangles On Sides of a Parallelogram at cut-the-knot
• Varignon and Wittenbauer Parallelograms by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Van Aubel's theorem Quadrilateral with four squares by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
• Parallelogram Quiz
• Definition and properties of a parallelogram with animated applet
• Interactive applet showing parallelogram area calculation interactive applet