# Parallelogram: Definition of a Parallelogram, Basic Properties of a Parallelogram, Shape of a Parallelogram, Types of Parallelogram (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Definition

- A Parallelogram is a two-dimensional shape in sides are parallel to each other.
- In Euclidean geometry, a parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides.
- In other words, we can define a parallelogram as a quadrilateral with two pairs of parallel sides.

## Basic Properties of a Parallelogram

- Total number of sides are four.
- Total number of vertices are four.
- Mutually parallel sides are two.
- The opposite angles are congruent.
- Area is equal to the multiplication of base and height.
- Perimeter is twice the sum of adjacent sides length.
- The sum of adjacent angles of a parallelogram is equal to 180 degrees.
- The sum of all the interior angles equals 360 degrees.

In the above figure and

Also, we have and ; and

Since are supplementary and are supplementary,

and

## Types of a Parallelogram

### Rhomboid

- The opposite pair of sides are parallel.
- The opposite sides of a rhomboid are also congruent.
- The diagonal divides the rhomboid into two congruent triangles.
- The opposite angles of a rhomboid are also congruent.
- The sum of interior angles of a rhomboid is equal to 360 degrees.
- A rhomboid becomes a rhombus if all the sides become equal and therefore a rhombus is always a rhomboid.

### Rectangle

- A parallelogram with four angles of equal size (right angles) .
- In a rectangle the diagonals are congruent.
- The opposite sides are equal in a rectangle.
- Each angle in the rectangle is the angle bisector of the opposite angle.

### Rhombus

- A parallelogram with four sides of equal length.
- A rhombus is an equilateral quadrilateral.
- An equilateral quadrilateral is one in which all the sides are equal.
- In case of a kite, when all the sides become equal in length the kite becomes a rhombus.

### Square

- A parallelogram with four sides of equal length.
- The angles of equal size (right angles) .
- The diagonals are perpendicular bisectors of each other.
- The lengths of the diagonals are equal.
- All such squares in which the diagonals are congruent and bisect the angles are termed as parallelogram.
- Every square is a rectangle and a rhombus.

## Area of the Parallelogram

In the given parallelogram b is the base and h is the height and it can be divided into a trapezoid and a right triangle, Also in the second figure a parallelogram has been rearranged into a rectangle.

Therefore, the area of a parallelogram is the same as that of a rectangle with the same base and height

In the above parallelogram the area is

## Perimeter of Parallelogram

Perimeter = 2 (a + b) units