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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
- Chord of a Circle – Definition, Properties & Examples
- 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
