A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides are parallel and equal in length. The diagonals bisect each other.

### Properties of Parallelogram

1. Each diagonal divides the quadrilateral into two congruent triangles with the same orientation.

2. The opposite sides are parallel and equal in length.

3. The diagonals bisect each other.

4. The opposite angles are equal in measure.

5. The sum of the squares of the sides equals the sum of the squares of the diagonals. (Parallelogram Law)

6. Adjacent angles are supplementary (180 degrees).

7. Square, Rectangle and Rhombus are special types of parallelograms.

### Perimeter & Area of Parallelogram

The perimeter of parallelogram is sum of the length of its sides. Perimeter = 2(L + B)

Area of parallelogram is multiplication of its longer side and distance between them. Area = L * H

### Parallelogram Law

It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. If ABCD is parallelogram, then

2(AB)2 + 2(BC)2 = (AC)2 + (BD)2

In case of rectangle and square, this law reduces to pythagoras theorem.