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In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. In Euclidean Geometry, the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The threedimensional counterpart of a parallelogram is a parallelepiped.
The etymology (in Greek παραλληλόγραμμον, a shape "of parallel lines") reflects the definition.
Contents
Properties
 Opposite sides of a parallelogram are equal in length.
 Opposite angles of a parallelogram are equal in measure.
 Adjacent angles are supplementary (add up to 180 degrees).
 The area, A, of a parallelogram is A = bh, where b is the base of the parallelogram and h is its height.
 Opposite sides of a parallelogram are parallel (by definition) and so will never intersect.
 The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
 The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.
 The diagonals of a parallelogram bisect each other.
 Any nondegenerate affine transformation takes a parallelogram to another parallelogram.
There is an infinite number of affine transformations which take any given parallelogram to a square.
 A parallelogram has rotational symmetry of order 2 (through 180°). If it also has two lines of reflectional symmetry then it must be a rhombus or a rectangle.
 The perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent
Types of parallelogram
 Rhomboid  A quadrilateral whose opposite sides are parallel and adjacent sides are unequal, and whose angles are not right angles
 Rectangle  A parallelogram with four angles of equal size (right angles).
 Rhombus  A parallelogram with four sides of equal length.
 Square  A parallelogram with four sides of equal length and four angles of equal size (right angles).
Proof that diagonals bisect each other
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