## Parallelogram Definition

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

In the figure, ABCD is a parallelogram as AB || CD (or AB parallel to CD) and AD || BC (or AD parallel to BC).

It is denoted by ||gm ABCD.

### Properties of parallelogram

###### 1. The opposite sides of a parallelogram are equal.

In the figure, ABCD is a parallelogram, where

**AB = CD and BC = AD**

###### 2. The opposite angles of a parallelogram are equal.

In the figure,

A = C and

B = D.

###### 3. Diagonals of a parallelogram bisect each other.

We will observe that in case OA – OC and OB – OD are either zero or so small that the same may be ignored.

Thus, in each case, **OA = OC and OB = OD**.

### Types of a parallelogram

Some special types of a parallelograms are:

#### 1. Rectangle

A rectangle is a parallelogram one of whose angles is a right angle.

In the adjoining figure, ABCD is a rectangle in which B = 90°

#### 2. Square

A square is a rectangle in which all sides are equal.

In given figure, ABCD is a square as

AB = BC = CD = DA and B = 90°

#### 3. Rhombus

Rhombus is a parallelogram whose all sides are equal.

In given below figure, ABCD is a rhombus as

AB = BC = CD = DA