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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.

## Examples of Quadrilateral

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

Quadrilateral | Shape |

Square | |

Rectangle | |

Parallelogram | |

Trapezium | |

Rhombus | |

Kite |

## Adjacent and Opposite Vertices of a Quadrilateral

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

Adjacent Vertices | Opposite Vertices |

$\text{A}$ and $\text{B}$ $\text{B}$ and $\text{C}$ $\text{C}$ and $\text{D}$ $\text{D}$ and $\text{A}$ | $\text{A}$ and $\text{C}$ $\text{B}$ and $\text{D}$ |

## Adjacent and Opposite Sides of a Quadrilateral

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

Adjacent Sides | Opposite Sides |

$\text{AB}$ and $\text{BC}$ (Common vertex $\text{B}$ $\text{BC}$ and $\text{CD}$ (Common vertex $\text{C}$ $\text{CD}$ and $\text{DA}$ (Common vertex $\text{D}$ $\text{DA}$ and $\text{AB}$ (Common vertex $\text{A}$ | $\text{AB}$ and $\text{CD}$ $\text{BC}$ and $\text{DA}$ |

## Adjacent and Opposite Angles of a Quadrilateral

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

Adjacent Angles | Opposite Angles |

$\angle \text{DAB}$ and $\angle \text{ABC}$(or $\angle \text{A}$ and $\angle \text{B}$) with common edge $\text{AB}$ $\angle \text{ABC}$ and $\angle \text{BCD}$(or $\angle \text{B}$ and $\angle \text{C}$) with common edge $\text{BC}$ $\angle \text{BCD}$ and $\angle \text{CDA}$(or $\angle \text{C}$ and $\angle \text{D}$) with common edge $\text{CD}$ $\angle \text{CDA}$ and $\angle \text{DAB}$(or $\angle \text{D}$ and $\angle \text{A}$) with common edge $\text{DA}$ | $\angle \text{DAB}$ and $\angle \text{BCD}$(or $\angle \text{A}$ and $\angle \text{C}$) $\angle \text{ABC}$ and $\angle \text{CDA}$(or $\angle \text{B}$ and $\angle \text{D}$) |

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

## Diagonals of a Quadrilateral

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

- Define the following
- Quadrilateral
- Opposite sides
- Adjacent sides
- Opposite angles
- Adjacent angles
- Opposite Vertices
- Adjacent vertices
- Diagonal

- How many vertices, sides, and angles do a quadrilateral have?
- What is the sum of all the angles of a quadrilateral?

## FAQs

### What is a quadrilateral?

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 $360^{\circ}$.

## Recommended Reading

- Properties of Triangle – Theorems & Examples
- How to Construct a Triangle(With Steps, Diagrams & Examples)
- Median of a Triangle(Definition & Properties)
- Altitude of a Triangle(Definition & Properties)
- Congruence of Triangles Criteria – SSS, SAS, ASA, RHS
- Similarity of Triangles Criteria – SSS, SAS, AA
- Types of Triangles – Definition & Examples
- What is Triangle in Geometry – Definition, Shapes & Examples
- Pair of Angles – Definition, Diagrams, Types, and Examples
- Construction of Angles(Using Protractor & Compass)
- Types of Angles in Maths(Acute, Right, Obtuse, Straight & Reflex)
- What is an Angle in Geometry – Definition, Properties & Measurement
- How to Construct a Tangent to a Circle(With Steps & Pictures)
- Tangent of a Circle – Meaning, Properties, Examples
- Angles in a Circle – Meaning, Properties & Examples
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- How to Draw a Circle(With Steps & Pictures)
- What is a Circle – Parts, Properties & Examples
- How to Construct a Perpendicular Line (With Steps & Examples)
- How to Construct Parallel Lines(With Steps & Examples)
- How To Construct a Line Segment(With Steps & Examples)
- What are Collinear Points in Geometry – Definition, Properties & Examples
- What is a Transversal Line in Geometry – Definition, Properties & Examples
- What are Parallel Lines in Geometry – Definition, Properties & Examples
- What is Concurrent lines in Geometry – Definition, Conditions & Examples
- What is Half Line in Geometry – Definition, Properties & Examples
- What is a Perpendicular Line in Geometry – Definition, Properties & Examples
- Difference Between Axiom, Postulate and Theorem
- Lines in Geometry(Definition, Types & Examples)
- What Are 2D Shapes – Names, Definitions & Properties
- 3D Shapes – Definition, Properties & Types