# What is Quadrilateral in Math(Definition, Shape & Examples)

This post is also available in: हिन्दी (Hindi)

There are many types of 2D figures you study in geometry and mensuration. A quadrilateral is one such type of a 2D plane figure, which has four edges(or sides), four angles, and four vertices.

Let’s understand what is the definition of quadrilateral in math and what are its different parts and properties.

## What is the Quadrilateral Definition in Math?

The word quadrilateral is consists of two words – ‘Qudra’ meaning ‘four’ and ‘Lateral’ meaning ‘from the sides or sides’. A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles. It is formed by joining four non-collinear points.

In the above figure, $\text{ABCD}$ is a quadrilateral has

• four sides $\text{AB}$, $\text{BC}$, $\text{CD}$, and $\text{DA}$
• four angles $\angle \text{DAB}$, $\angle \text{ABC}$, $\angle \text{BCD}$, and $\angle \text{CDA}$(or simply $\angle \text{A}$, $\angle \text{B}$, $\angle \text{C}$, and $\angle \text{D}$)
• four vertices $\text{A}$, $\text{B}$, $\text{C}$, and $\text{D}$

The quadrilateral $\text{ABCD}$ can also be named as $\text{BCDA}$, $\text{CDAB}$, or, $\text{DABC}$. But it cannot be named as $\text{ACBD}$ or $\text{DBAC}$, since they change the order of vertices in which a quadrilateral is formed.

As discussed above, a quadrilateral has four edges(or sides), four angles, and four vertices. There are various types of quadrilaterals. Examples of a quadrilateral are

The vertices that are adjacent to each other and are joined by a line segment called an edge(or a side) are called adjacent vertices of a quadrilateral. The vertices that are not connected or joined by the sides of a quadrilateral are called opposite vertices.

A quadrilateral in the above figure has

The sides(or edges) of a quadrilateral that have a vertex in common are known as adjacent sides or adjacent edges of a quadrilateral. A quadrilateral’s sides(or edges) that do not share a common vertex are known as opposite sides or edges of a quadrilateral.

A quadrilateral in the above figure has

The angles of a quadrilateral that have a common edge (or side) are known as adjacent angles of a quadrilateral. The angles that do not share a common edge(or side) are known as opposite angles of a quadrilateral.

A quadrilateral in the above figure has

Note: The sum of angles in a quadrilateral is $360^{\circ}$.

The line segments joining the opposite vertices of a quadrilateral are called diagonals of a quadrilateral.

In the above figure, the two diagonals of a quadrilateral $\text{ABCD}$ are $\text{AC}$ and $\text{BD}$.

## Key Takeaways

• A quadrilateral has four sides
• A quadrilateral has four angles
• A quadrilateral has four vertices
• A quadrilateral has two diagonals
• Vertices sharing a common side are called adjacent vertices
• Vertices that do not share a side are called opposite vertices
• Sides sharing a common vertex are called adjacent sides
• Sides that do not share a common vertex are called opposite sides
• Angles sharing a common side are called adjacent angles
• Angles that do not share a common side are called opposite vertices
• Lines joining opposite vertices are called diagonals
• The diagonals of a quadrilateral intersect each other
• The sum of four angles of a quadrilateral is $360^{\circ}$

## Practice Problems

1. Define the following
• Opposite sides
• Opposite angles
• Opposite Vertices
• Diagonal
2. How many vertices, sides, and angles do a quadrilateral have?
3. What is the sum of all the angles of a quadrilateral?

## FAQs A quadrilateral is a closed two-dimensional figure that has four sides, four angles, and four vertices. A few examples of quadrilaterals are square, rectangle, and rhombus.

### What is the sum of the interior angles in a quadrilateral?

In any type of quadrilateral, the sum of the interior angles is always equal to $360^{\circ}$.

### What are the three attributes of a quadrilateral?

The three important attributes of a quadrilateral are:
a) Four sides
b) Four Vertices
c) The sum of the interior angles should be equal to $360^{\circ}$.

## Conclusion

A quadrilateral is a closed two-dimensional figure that has four sides, four angles, and four vertices. The line segments joining the opposite vertices of a quadrilateral are called diagonals. A quadrilateral has two intersecting diagonals and the sum of the interior angles is $360^{\circ}$.