parallelogram

A parallelogram is a quadrilateral whose opposite sides are parallel.

Some special parallelograms have their own names: squares, rectangles, rhombuses. A rectangle is a parallelogram whose all angles are equal (i.e. ${90}^{\circ }$), a rhombus is a parallelogram whose all sides are equal, and a square is a parallelogram that is a rectangle and a rhombus at the same time.

Every parallelogram have their opposite sides and opposite angles equal. Also, adjacent angles of a parallelogram always add up to ${180}^{\circ }$, and the diagonals bisect each other.

A base of a parallelogram is one of its sides. Any side of a parallelogram can be selected as its base. Once a base has been selected, the height of the parallelogram is defined to be the length of any line segment perpendicular to the base which extends from the base to the opposite side parallel to the base. The area of a parallelogram with base length $b$ and height $h$ is given by the formula  $A=bh$.

There is also a neat relation between the length of the sides and the lengths of the diagonals called the parallelogram law.

Title	parallelogram
Canonical name	Parallelogram
Date of creation	2013-03-22 12:02:21
Last modified on	2013-03-22 12:02:21
Owner	drini (3)
Last modified by	drini (3)
Numerical id	11
Author	drini (3)
Entry type	Definition
Classification	msc 51-00
Related topic	ParallelogramTheorems
Related topic	Quadrilateral
Related topic	Rectangle
Related topic	Rhombus
Related topic	Square
Related topic	ParallelogramLaw
Related topic	Kite
Related topic	Rhomboid
Related topic	ProofOfParallelogramTheorems
Related topic	Parallelotope