## What are Quadrilaterals?

Quadrilaterals are one type of polygon which has four sides and four vertices and four angles along with 2 diagonals. There are various types of quadrilaterals.

## Types of Quadrilaterals

The classification of quadrilaterals are dependent on the nature of sides or angles of a quadrilateral and they are as follows:

- Trapezium
- Kite
- Parallelogram
- Square
- Rectangle
- Rhombus

### Polygons

A simple **closed curve **made up of only** line segments** is called a **polygon**.

Various examples of polygons are Squares, Rectangles, Pentagons etc.

Note:

The sides of a polygon do not cross each other.

For example, the figure given below is not a polygon because its sides cross each other.

### Classification of Polygons on the Basis of Number of Sides / Vertices

Polygons are classified according to the number of sides they have. The following lists the different types of polygons based on the number of sides they have:

- When there are three sides, it is
**triangle** - When there are four sides, it is
**quadrilateral** - When there are fives sides, it is
**pentagon** - When there are six sides, it is
**hexagon** - When there are seven sides, it is
**heptagon** - When there are eight sides, it is
**octagon** - When there are nine sides, it is
**nonagon** - When there are ten sides, it is
**decagon**

### Diagonals

A **diagonal** is a line segment connecting two **non-consecutive vertices** of a **polygon**.

As we can see for the above quadrilateral, if we join one of the diagonals of the quadrilateral, we get two triangles.

The sum of all the interior angles of the two triangles is equal to the sum of all the interior angles of the quadrilateral, which is equal to 360∘ = (4−2)×180∘.

So, if there is a polygon which has** n sides**, we can make

**(**which will perfectly cover that polygon.

*n*– 2) non-overlapping triangles### Elements of a Parallelogram

- There are
**four sides**and**four angles**in a parallelogram. - The
**opposite sides**and**opposite angles**of a parallelogram are**equal**. - In the parallelogram ABCD, the sides ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯¯CD are
**opposite**sides and the sides ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯BC are**adjacent sides**. - Similarly, ∠ABC and ∠ADC are
**opposite angles**and ∠ABC and ∠BCD are**adjacent angles**.

### Angles of a Parallelogram

The **opposite angles **of a parallelogram are **equal**.

In the parallelogram ABCD, ∠ABC=∠ADC and ∠DAB=∠BCD.

The **adjacent angles **in a parallelogram are** supplementary**.

∴ In the parallelogram ABCD, ∠ABC+∠BCD=∠ADC+∠DAB=180∘

## Properties of Special Parallelograms

### Rectangle

A **rectangle** is a **parallelogram** with **equal angles** and each angle is** equal to 90**∘.

Properties:

**Opposite sides**of a rectangle are**parallel**and**equal**.- The length of
**diagonals**of a rectangle is**equal**. - All the
**interior angles**of a rectangle are**equal to 90**∘. - The
**diagonals**of a rectangle**bisect**each other at the point of intersection.

### Square

A **square **is a** rectangle** with **equal sides**. All the properties of a rectangle are also true for a square.

In a square the diagonals:

- bisect one another
- are of equal length
- are perpendicular to one another