# Types of Quadrilaterals

By the end of this lesson, you will be able to

- define quadrilateral.
- classify different types of quadrilateral.
- interpret properties of quadrilateral.
- demonstrate examples of quadrilateral.

## Quadrilateral

A four-sided polygon with four vertices is a quadrilateral. A quadrilateral is a special polygon in terms of Edges and angles.

## Classification of Quadrilaterals

Quadrilaterals are generally divided into two parts in terms of self-intersecting:

- Simple quadrilaterals (none self-intersecting)
- Complex quadrilaterals (self-intersecting)

### Simple Quadrilateral

A quadrilateral is said to be a simple quadrilateral if it is not self-intersecting.

Simple quadrilaterals are, again, divided into two parts:

- Convex Quadrilaterals
- Concave Quadrilaterals

### Convex Quadrilaterals

A convex quadrilateral is a quadrilateral in which all interior angles are less than 180° and both diagonals lie inside the quadrilateral.

### Properties of Convex Quadrilateral

A few properties of convex properties are given below:

- Four edges or sides.
- Four vertices or corners.
- Two diagonals.
- Two diagonals both must lie inside the quadrilateral.
- Each interior angle is less than 180°.
- All interior angles add up to 360°.

### Concave Quadrilaterals

A concave quadrilateral is a quadrilateral in which one of the two diagonals is outside the quadrilateral and one interior angle is greater than 180° and less than 360°.

An angle θ, 180°<θ<360° and a diagonal is outside of quadrilateral.

A concave quadrilateral

### Complex Quadrilateral

A complex quadrilateral is a quadrilateral if it is self-intersecting.

It is also well-known as crossed-quadrilateral.

In a complex quadrilateral, there are two reflex and other two angles are acute among the four interior angles.

And these four interior angles add up to 720°.

A complex quadrilateral

Another complex quadrilateral

### Irregular Quadrilateral

An irregular quadrilateral is a quadrilateral with no parallel sides.

An irregular quadrilateral in the figure because this quadrilateral has no parallel sides.

There are several types of quadrilaterals in plane geometry.

And there are few properties in common and uncommon for different types of quadrilaterals.

All quadrilaterals must have, for instance, four edges and four vertices. And these are common properties for all quadrilaterals.

All interior angles, for example, are less than 180^{0} for some quadrilaterals.

On the other hand, one interior angle is greater than 180^{0} for several quadrilaterals.

For some quadrilaterals, two diagonals both lie inside the quadrilateral.

One of the two diagonals, on the other hand, lies outside the quadrilateral.

These are some uncommon properties depending on types of quadrilaterals.