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

quadrilateral definition

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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.

quadrilateral definition

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

QuadrilateralShape
SquareCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples) TROkBPTgdGm9nC09M8FkVxOG7GBN3Ge10TBrzK
RectangleCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples) vuFxjVXrNmKtuU0aCMWrE0 kN8tI7qpufvsFLfmCd7D0exxBeDVCCKPvJQ7p5M77LAbulY8nMlHB28RqGYUkAioUjr3dQosgfUwHiix8rHP jdZtBN79W04f6C0vZqLgZiL5DDW6ApPDQRJ4I02oeKIg4WjsBH5SeLlQiySDeaUOOdZHSZYwA E6avVREg
ParallelogramCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples) 4ns5uSHe
TrapeziumCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples) YJZVSVyDHN9GmK evtjZNsL9gM0tDu31ivEGBkmSBqlIh2Rab790A0ruaUW6hLMLkti4uRTMhfO3 E778PyXVxzQFZ7HO5aCdLreGEyz3g Wgb0I OLfg3E7NUErWuSJZSiSkDRcDFlQJS 1h4cbi1V15PGWMQzcgP5bAorhsMAol722ER c6MoKBisZAA
RhombusCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples)
KiteCodingHero - What is Quadrilateral in Math(Definition, Shape & Examples) tNHu d18kw8Wguyg7u Cy7vQfJD1Hy5YCpfCoxwHiSduooeKgo5m3pA1C7TgpsxsB5loDvCJp5LG2PjuWNKQXRXYvJC0tv6oiSNB5h5iGuyzCoKpA74wYeZr1DdL12RFegNCXBSwO9Jqn5f98WMneO8 ttGVdnncu7CnulPFhKdC1pt7f3HUD2Lo5ynGLg

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.

quadrilateral definition

A quadrilateral in the above figure has

Adjacent VerticesOpposite 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.

quadrilateral definition

A quadrilateral in the above figure has

Adjacent SidesOpposite 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.

quadrilateral definition

A quadrilateral in the above figure has

Adjacent AnglesOpposite 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.

quadrilateral definition

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 $360^{\circ}$
Famous Mathematicians

Practice Problems

  1. Define the following
    • Quadrilateral
    • Opposite sides
    • Adjacent sides
    • Opposite angles
    • Adjacent angles
    • Opposite Vertices
    • Adjacent 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

What is a quadrilateral?

quadrilateral definition

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 $360^{\circ}$.

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