# Parallelogram

A quadrangle, the opposite sides of which are parallel, is called a parallelogram.
Each couple of opposite sides in a parallelogram are equal.
In order to ascertain whether a quadrangle is parallelogram, we will use the following indications (criteria):
-if the two couples of opposite sides in a quadrangle are equal, then this quadrangle is a parallelogram;
-if two opposite sides in a quadrangle are parallel and equal, then this quadrangle is a parallelogram
-if, in a quadrangle, the diagonals intersect one another in the middle, then this quadrangle is a parallelogram
A quadrangle which has one right angle is called rectangle.
The following statement is valid: If a parallelogram is a rectangle, then its diagonals are equal in length Vice versa, if the diagonals of a parallelogram are equal in length, then this parallelogram is a rectangle.
A parallelogram that has two contiguous sides equal in length, is called rhomb. The following statement is valid about the rhomb: If a parallelogram is a rhomb, then its diagonals are perpendicular. Vice versa, if the diagonals of a parallelogram are perpendicular, then this parallelogram is a rhomb.
A square may be considered as rectangle which has contiguous sides equal in length, or a rhomb that has right angle. Therefore, a square has all the characteristics of a rectangle and a rhomb.

#### Parallelogram formulae

Perimeter of a parallelogram:

P = 2a + 2b

Area of a parallelogram formula:

S = b.h = ab.sinA

The sum of two contiguous angles is 180°

A + B = 180° and A + D = 180°

Dependency of diagonals and sides of a parallelogram formula

p2 + q2 = 2(a2 + b2)

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