# Parallelogram

In this article you will learn the concept of parallelogram, types of parallelogram and properties of parallelogram.

Before learning parallelogram, let’s understand the term “parallel”.

**What is parallel?**

Parallel lines are lines in a plane that never intersect or touch each other at any point. They are always the same distance apart and go side by side without ever touching each other.

## What is parallelogram?

A parallelogram is a special type of quadrilateral that has at least two sides that are parallel to each other.**Related Topic: Identifying Quadrilaterals**

## Six Properties of Parallelogram

1. Opposite sides of Parallelogram are parallel to each other. Here,** AB ∥ CD and AD ∥ BC**

2. Opposite sides are congruent, means opposite sides are equal in length. **AB = CD and AD = BC**

3. Opposite angles are congruent, means opposite angles are equal in measure. **angle B = angle D and angle A = angle C**

4. Adjacent angles of a parallelogram are supplementary. Supplementary angles means two angles that add up to 180.**Angle A + Angle B = 180°**

**Angle B + Angle C = 180°**

**Angle C + Angle D = 180°**

**Angle D + Angle A = 180°**

5. The diagonals of a parallelogram bisect each other. **AC and BD bisect each other**.

6. Each diagonal of a parallelogram separates it into two equal triangles. **△ACD ≅ △ABC****Related Topic: Point Lines Line Segments and Rays**

## 3 Types of Parallelogram

#### Rhombus

- All sides are equal and opposite sides are parallel.
- Opposite angles are equal.
- The diagonals bisect each other at right angles.
- Here AB = BC = CD = DA. So ABCD is a rhombus.

#### Rectangle

- All angles are 90 degrees.
- Opposite sides are parallel and equal.
- Diagonals are congruent.
- Each diagonal is angle bisector of opposite angle
- Here AB = DC and AD = BC
- Diagonal AC = Diagonal BD

#### Square

- All sides are equal in length
- Each interior angle is right angle [90 degrees]
- Length of diagonals is equal
- Diagonals are perpendicular bisectors of each other
- Every square is a rectangle and a rhombus

## Area of Parallelogram

**Area = Base x Height**[Area = b x h]

**Example**: A parallelogram has a base of 7 m and is 4 m high, what is its Area?

Area = 7 m x 4 m = 28m^{2}

## Perimeter of a Parallelogram

**2 x (base + side length)**or Perimeter = 2(b+s)

**Example**:A parallelogram has a base of 15 cm and a side length of 5 cm, what is its Perimeter?

Perimeter = 2 × (15 cm + 5 cm) = 2 × 20 cm = 40 cm

**Try Now!**

Example 1: A parallelogram has a base of 21 cm and a side length of 7 cm, what is its Perimeter?

Example 2: A parallelogram has a base of 16 m and is 13 m high, what is its Area?