Definition Properties Types and Examples of Quadrilaterals
A quadrilateral is simply a 2-dimensional geometrical figure consisting of "four sides". The term quadrilateral is derived from two words i.e. quad = four and lateral = side. A Quadrilateral is a closed, flat shape in which the lines connect, and has straight sides.
Talking about the properties of a quadrilateral, these are as follows:
A polygon with four straight sides also termed as edges
it has four vertices also termed as corners
A quadrilateral has four interior angles that sums up to 360 degrees
What is a Quadrilateral Shape?
A Quadrilateral is a polygon of 2D geometrical figures consisting of "four sides". A quadrilateral can sometimes also be known as:
Quadrangle derived from 2 words i.e. quad meaning ("four angles"), and rangle that sounds like "triangle"
Tetragon derived from 2 words i.e. ("four polygon"), and gon that sounds like "hexagon", "pentagon", octagon etc.
Types of Quadrilaterals and Their Properties
There are various special kinds of quadrilateral. The Quadrilaterals and its classification are as below.
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Paralleogram
A parallelogram is a simple quadrilateral under the Euclidean geometry in which both pairs of opposite sides are parallel to one another. A parallelogram also consists of the following properties:
Opposite sides of a parallelogram are congruent
Opposite angles are in congruence
Adjacent angles are supplementary, meaning that they make 180 degree measurement
The diagonals intersect each other.
Rectangle
A rectangle is one form of a parallelogram only. Since a rectangle has four right angles, thus all rectangles are also parallelograms and quadrilaterals. On the contrary, not all parallelograms and quadrilaterals are rectangles. A rectangle consists of the following properties:
Opposite sides are in congruence
Opposite angles are in congruence
Adjacent angles are supplementary, meaning that they make 180 degree measurement
The diagonals intersect each other.
The diagonals are in congruence
Square
A square is a 2 dimensional, closed geometric object consisting of 4 equal sides. A Square is most frequently seen around us in real life in the form of a wall clock, chessboard, bread slice etc. A square consists of the following properties:
A square consists of 4 sides and 4 angles
Length of all the sides of a square are equal in measurement
All angles are at right angles and are 90 degrees each
All interior angles are equal in measurement and the sum of all the interior angles is 360°.
A square can be described as a rhombus which is also a rectangle – specifically, a parallelogram with 4 congruent sides and 4 right angles.
Rhombus
A rhombus is a parallelogram with four sides in congruence to each other. Rhombus is also known as rhombi in its plural sense. A rhombus also consists of the following properties:
Opposite sides of a rhombus are congruent
Opposite angles are in congruence
Adjacent angles are supplementary, meaning that they make 180 degree measurement
The diagonals bisect each other at right angles.
In some textbooks you will find a kite has a minimum of 2 pairs of adjacent congruent sides, thus a rhombus is a special case of a kite.)
Trapezoid
A trapezoid is a unique kind of a quadrilateral that has exactly one pair of parallel sides. There may be some ambiguity with respect to this term depending on the country you're from. This is to say, in India and Britain, they call it trapezium; whereas, in America, trapezium generally means a quadrilateral polygon with no parallel sides.)
Isosceles Trapezoid
An isosceles trapezoid is kind of a trapezoid whose non-parallel sides are in congruence to each other. A kite is one type of a quadrilateral consisting of exactly two pairs of adjacent sides congruent. This description of a quadrilateral shape excludes rhombi.
FAQs on What Are Quadrilaterals in Geometry
1. What are quadrilaterals?
A quadrilateral is a polygon with four sides, four vertices, and four angles. In geometry, quadrilaterals are 2D closed shapes formed by four line segments. Examples of quadrilaterals include:
- Square
- Rectangle
- Parallelogram
- Rhombus
- Trapezium (Trapezoid)
2. What is the sum of the interior angles of a quadrilateral?
The sum of the interior angles of a quadrilateral is 360°. This result comes from the polygon angle sum formula: (n − 2) × 180°. For a quadrilateral, n = 4, so (4 − 2) × 180° = 2 × 180° = 360°. This rule applies to all types of quadrilaterals.
3. What are the different types of quadrilaterals?
The main types of quadrilaterals are classified based on their sides and angles. These include:
- Square – four equal sides and four right angles
- Rectangle – opposite sides equal and four right angles
- Parallelogram – opposite sides parallel and equal
- Rhombus – four equal sides, opposite angles equal
- Trapezium (Trapezoid) – at least one pair of parallel sides
- Kite – two pairs of adjacent equal sides
4. How do you find the area of a quadrilateral?
The area of a quadrilateral depends on its type and given measurements. Common formulas include:
- Square: side × side
- Rectangle: length × width
- Parallelogram: base × height
- Trapezium: ½ × (sum of parallel sides) × height
5. What is the difference between a square and a rectangle?
The main difference is that a square has all four sides equal, while a rectangle has only opposite sides equal. Both shapes have four right angles (90°). In summary:
- Square: all sides equal, all angles 90°
- Rectangle: opposite sides equal, all angles 90°
6. What are the properties of a parallelogram?
A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Its key properties are:
- Opposite sides are equal and parallel
- Opposite angles are equal
- Consecutive angles are supplementary (sum to 180°)
- Diagonals bisect each other
7. What is a trapezium (trapezoid) in geometry?
A trapezium (trapezoid) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the perpendicular distance between them is the height. The area formula is ½ × (sum of parallel sides) × height. Trapeziums are commonly studied in coordinate geometry and mensuration.
8. How many diagonals does a quadrilateral have?
A quadrilateral has 2 diagonals. The number of diagonals in a polygon is given by the formula n(n − 3)/2. For n = 4: 4(4 − 3)/2 = 4 × 1/2 = 2. Diagonals connect opposite vertices of the quadrilateral.
9. What is a kite in quadrilaterals?
A kite is a quadrilateral with two pairs of adjacent equal sides. Its important properties include:
- One pair of opposite angles is equal
- Diagonals are perpendicular
- One diagonal bisects the other
10. What are some real-life examples of quadrilaterals?
Quadrilaterals appear frequently in real life as four-sided shapes. Common examples include:
- Windows and doors – rectangles
- Floor tiles – squares
- Bridges and frames – trapeziums
- Diamond-shaped signs – rhombuses
