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A quadrilateral is a closed shape and a type of polygon that is formed by four non-colinear points having four sides, four vertices, and four angles. There are various types of quadrilaterals based on their properties. Squares, rectangles, parallelograms, and rhombus are a few types of quadrilaterals.

Let’s learn about different types of quadrilaterals and their properties with their examples.

## Different Types of Quadrilaterals

The quadrilaterals are broadly divided into two types.

- Concave Quadrilaterals
- Convex Quadrilaterals

### Concave Quadrilaterals

In concave quadrilaterals, one interior angle is greater than $180^{\circ}$. A quadrilateral is called a concave quadrilateral if at least one diagonal, i.e. the line segment joining the vertices is not a part of the same region of the quadrilateral.

### Convex Quadrilaterals

In convex quadrilaterals, each interior angle is less than $180^{\circ}$. A quadrilateral is convex if both diagonals lie in the same region of the quadrilateral.

The convex quadrilaterals are further divided into six types. These six types of quadrilaterals are

- Parallelogram
- Trapezium
- Rhombus
- Rectangle
- Square
- Kite

Let’s learn about these in detail.

### Parallelogram

A quadrilateral in which the opposite sides are parallel to each other and equal in length is called a parallelogram. The sum of its consecutive angles in a parallelogram is equal to $180^{\circ}$. The diagonals of a parallelogram intersect each other at the midpoint.

Examples of a parallelogram are the flat surfaces of tables, desks, etc.

The following are some of the properties of parallelograms.

- Two pairs of parallel sides
- Opposite sides of equal lengths
- Opposite angles that are equal
- Two diagonals bisect each other, i.e., one diagonal divides the other diagonal into exactly two halves.

In the above figure, $\text{ABCD}$ is a parallelogram, where $\text{AB} || \text{CD}$ and $\text{BC} || \text{DA}$. The diagonals intersect at the middle point $\text{O}$ where $\text{AO} = $\text{OC}$ and $\text{BO}$ = $\text{OD}$.

In mensuration, a parallelogram has two types of measurements.

- Perimeter of Parallelogram
- Area of a Parallelogram

### Trapezium

A quadrilateral in which one pair of opposite sides parallel, is called a trapezium. In trapezium, two pairs out of four pairs of adjacent angles are supplementary. The sides that are parallel to each other are called bases and the sides that are not parallel to each other are called legs.

Examples of a trapezium are drawings of bridges, handbags, etc.

The following are some of the properties of trapezium.

- One pair of opposite sides are parallel
- The sum of two pairs of adjacent angles is $180^{\circ}$

In the above figure, $\text{PQRS}$ is a trapezium, where $\text{PQ} || \text{RS}$, $\angle \text{P} + \angle \text{S} = 180^{\circ}$, and $\angle \text{Q} + \angle \text{R} = 180^{\circ}$.

In mensuration, a trapezium has two types of measurements.

### Rhombus

A rhombus is also known as an equilateral quadrilateral or a diamond that has all four sides of equal lengths. In a rhombus, the opposite sides are parallel and the opposite angles are equal.

Examples are the plane surfaces of mirrors, section-based football fields, etc.

The following are the properties of a rhombus.

- All four sides are equal in length
- Opposite angles are equal
- Diagonals are unequal and perpendicular to each other
- The diagonals bisect each other
- Opposite sides are equal and parallel

In the above figure $\text{PQRS}$ is rhombus, where $\text{PQ} || \text{RS}$ and $\text{PS} || \text{QR}$. All the sides are equal to each other, i.e., $\text{PQ} = \text{QR} = \text{RS} = \text{SP}$.

In mensuration, a rhombus has two types of measurements.

### Rectangle

In a rectangle opposite sides are of equal length and parallel to each other. The angles of a rectangle are equal in measure and are right-angled i.e. they measure $90^{\circ}$.

Examples of a rectangle are dollar bills, a playing card, flat surface of a board, etc.

The following are the properties of a rectangle.

- Two pairs of parallel sides
- All four angles are right angles, that is, they measure $90^{\circ}$
- Opposite sides are of equal lengths
- Two equal diagonals
- The two diagonals bisect each other in equal halves

In the above figure, $\text{ABCD}$ is a rectangle where, $\text{AB} || \text{CD}$, $\text{AB} = \text{CD}$, $\text{BC} || \text{DA}$, and $\text{BC} = \text{DA}$. All the angles are $90^{\circ}$, i.e., $\angle \text{A} = \angle \text{B} = \angle \text{C} = \angle \text{D} = 90^{\circ}$.

In mensuration, a rectangle has two types of measurements.

### Square

In a square, all sides are equal in length and all angles are of equal measure, which $90^{\circ}$ each.

An example of a square is a chessboard.

The following are the properties of a square.

- All sides are equal in length
- All four internal angles measure $90^{\circ}$
- Diagonals are equal and perpendicular to each other

In the above figure $\text{PQRS}$ is a square, where $\text{PQ} = \text{QR} = \text{RS} = \text{SP}$, and $\text{PQ} || \text{RS}$ and $\text{PS} || \text{QR}$. All the angles are $90^{\circ}$, i.e., $\angle \text{P} = \angle \text{Q} = \angle \text{R} = \angle \text{S} = 90^{\circ}$.

In mensuration, a square has two types of measurements.

### Kite

A kite has two pairs of adjacent sides are of equal length. A kite is also called a dart or an arrowhead because of its shape.

A real-life example is a kite itself.

The following are the properties of a kite.

- Two pairs of adjacent sides equal
- Diagonals are perpendicular to each other

In the above figure $\text{ABCD}$ is a kite where, $\text{AB} = \text{DA}$, and $\text{BC} = \text{CD}$.

In mensuration, a kite has two types of measurements.

## Key Takeaways

Name of the Quadrilateral | Shape of the Quadrilateral | Properties of the Quadrilateral |

Parallelogram | Opposite sides are parallel Opposite sides are equal Opposite angles are equal Adjacent angles are supplementary | |

Trapezium | One pair of opposite sides are parallel Two pairs of adjacent angles are supplementary | |

Rhombus | All sides are equal Opposite sides are equal Diagonals are unequalDiagonals bisect each other at right angles | |

Rectangle | Opposite sides are equal Opposite sides are parallel Diagonals are equal Measure of each angle is $90^{\circ}$ | |

Square | All sides are equal Opposite sides are parallel Measure of each angle is $90^{\circ}$ Diagonals are equal Diagonals bisect each other at $90^{\circ}$ | |

Kite | Two pairs of adjacent sides are equal One pair of opposite angles are equal |

## Practice Problems

- What is a convex quadrilateral?
- What is a concave quadrilateral?
- Write down the important properties of
- Parallelogram
- Trapezium
- Rhombus
- Rectangle
- Square
- Kite

## FAQs

### What are the 6 types of quadrilaterals?

The 6 types of quadrilaterals are parallelogram, trapezium, rhombus, rectangle, square, and kite.

### Which quadrilateral has four congruent sides?

The quadrilaterals having all four sides congruent are square and rhombus.

### What kind of quadrilateral has 4 equal sides and 4 right angles?

A quadrilateral that has 4 equal sides and 4 right angles is a square.

### Do kites have parallel sides?

No, there are no parallel sides for a kite.

## Conclusion

The quadrilaterals are broadly categorized as concave and convex quadrilaterals. The convex quadrilaterals are further divided into six types, each having its own unique shape and properties. The six types of quadrilaterals are parallelogram, trapezium, rhombus, rectangle, square, and kite.

## Recommended Reading

- 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
- Angle Bisector of a Triangle – Definition, Properties & Examples
- What is Quadrilateral in Math(Definition, Shape & Examples)
- 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)
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- How to Draw a Circle(With Steps & Pictures)
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- 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
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- Lines in Geometry(Definition, Types & Examples)