How to Identify and Classify Quadrilaterals in Geometry
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? Meaning, Types & Properties
1. What is a quadrilateral in geometry?
A quadrilateral is a two-dimensional polygon that has exactly four sides, four angles, and four vertices (corners). It is a closed shape formed by connecting four straight line segments. The sum of all interior angles in any convex quadrilateral is always 360 degrees.
2. What are the basic properties that all quadrilaterals share?
Every quadrilateral, regardless of its specific type, has the following fundamental properties:
It has four sides and four vertices.
The sum of its four interior angles is equal to 360°.
It has two diagonals, which are line segments connecting opposite vertices.
3. What are the main types of quadrilaterals studied in the CBSE syllabus?
The primary types of quadrilaterals covered in the CBSE curriculum include:
Parallelogram: A quadrilateral with two pairs of parallel opposite sides.
Rectangle: A parallelogram where all four angles are right angles (90°).
Square: A rectangle with all four sides of equal length.
Rhombus: A parallelogram with all four sides of equal length.
Trapezium (or Trapezoid): A quadrilateral with at least one pair of parallel sides.
Kite: A quadrilateral with two distinct pairs of equal-length adjacent sides.
4. How do you differentiate between a parallelogram, rectangle, rhombus, and square?
These shapes are all parallelograms but differ in their specific properties. A parallelogram is the base category with opposite sides parallel and equal. A rectangle is a parallelogram with all angles being 90°. A rhombus is a parallelogram with all sides being equal. A square is the most specific type; it is both a rectangle (all angles 90°) and a rhombus (all sides equal), making it a regular quadrilateral.
5. Why is the sum of the interior angles of any convex quadrilateral always 360 degrees?
This fundamental property can be understood by drawing a single diagonal inside any convex quadrilateral. This diagonal divides the quadrilateral into two distinct triangles. According to the angle sum property of a triangle, the sum of interior angles in each triangle is 180°. Since the quadrilateral is now composed of two triangles, the sum of its angles is the sum of the angles of these two triangles, which is 180° + 180° = 360°.
6. What is the difference between a convex and a concave quadrilateral?
The key difference lies in their interior angles and diagonals. In a convex quadrilateral, all interior angles are less than 180°, and both of its diagonals lie completely inside the figure. In a concave quadrilateral, one of the interior angles is a reflex angle (greater than 180°), and one of its diagonals lies partially or entirely outside the figure.
7. Can you provide some real-world examples of different quadrilaterals?
Yes, quadrilaterals are all around us. For example:
Rectangle: A door, a window, a book cover, or a smartphone screen.
Square: A standard chessboard square, a slice of processed cheese, or a wall tile.
Rhombus: The shape of a diamond in a deck of cards or certain patterns in floor tiles.
Trapezium: The shape of a popcorn box, a bucket, or some truss bridge sections.
Kite: The classic shape of a flying kite.
8. How is a trapezium different from a parallelogram?
The primary distinction is the number of parallel sides. A parallelogram must have two pairs of opposite sides that are parallel to each other. In contrast, a trapezium (also known as a trapezoid) is defined as having only one pair of opposite parallel sides. Therefore, every parallelogram is a special type of quadrilateral, but a trapezium is not a parallelogram.
9. What are the unique properties of a kite?
A kite is a unique quadrilateral defined by having two pairs of equal-length sides that are adjacent to each other. Its key properties are:
The diagonals are perpendicular to each other.
One of the diagonals is the perpendicular bisector of the other diagonal.
It has one pair of equal opposite angles (the angles between the unequal sides).
