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Types of Quadrilaterals
There are various types of quadrilaterals based on their properties. Squares, rectangles, parallelograms, rhombus are a few types of quadrilaterals. A polygon with four sides and four vertices is called a quadrilateral. The word is derived from two Latin words - "Quadri" and "Latus" meaning a variant of four and sides respectively. In quadrilaterals, the lengths and angles might be different or the same. Tetragon and Quadrangle are the other names of a quadrilateral.
Let's learn about some particular types of quadrilaterals in this lesson by learning about their names and properties. Let's begin!
|1.||Definition of Quadrilaterals|
|2.||Properties of Quadrilaterals|
|3.||Types of Quadrilaterals|
|12.||FAQs on Types of Quadrilaterals|
Definition of Quadrilaterals
In math, a quadrilateral is a polygon having four sides, four vertices, and four angles. A quadrilateral can be defined in two ways:
- A quadrilateral is a closed shape that is obtained by joining four points among which any three points are non-collinear.
- A quadrilateral is a closed 2D shape with four vertices and four sides.
Properties of Quadrilaterals
In this section, let us discuss quadrilaterals' properties in general, which applies to all types of quadrilaterals. The properties of quadrilaterals are listed below:
- They have four sides
- They are 2D shapes
- They have four vertices
- They have two diagonals
- The sum of all the interior angles of a quadrilateral is always 360°.
Now, let us see the types of quadrilaterals.
Types of Quadrilaterals
There are six basic types of quadrilaterals, and they are:
Let's discuss each one in detail in the following sections.
A parallelogram is a type of quadrilateral with the opposite sides parallel to each other and equal in length. It is a four-sided shape with opposite sides equal in length along with opposite angles equal and the sum of its consecutive angles is equal to 180°. The diagonals of a parallelogram intersect each other at the midpoint. Examples of a parallelogram are the flat surfaces of tables, desks, etc.
Properties of a Parallelogram
Some of the properties of the parallelograms are given as:
- 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 below figure PQRS, we can see that PQ II RS and PS II QR. The diagonals intersect at the middle point O where PO = OR and QO = OS
A quadrilateral with one pair of opposite sides parallel, its longest side sliding downwards, a triangle lookalike with its top sliced off, and two sloping sides as edges connecting with the parallel sides is called a trapezium. 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.
Properties of a Trapezium
Some of the properties of the trapezium are given below:
- Contains four vertices and four edges
- One pair of opposite sides are parallel
- The sum of adjacent angles is 180°
In the trapezium PQRS, side PQ is parallel to RS.
A rhombus is also known as an equilateral quadrilateral or a diamond that contains all four sides of equal lengths. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Some of the real-life examples are the plane surfaces of mirrors, section-based football fields, etc.
Properties of a Rhombus
Some of the properties of the rhombus are given below:
- Opposite angles are equal
- All four sides are equal in length
- Diagonals are congruent and perpendicular to each other
- The diagonals bisect each other dividing it into two halves
- Opposite sides are equal and parallel
In the Rhombus PQRS, we can find out that PQ II RS and PS II QR. All the sides are equal to each other PQ = QR = RS = SP
A rectangle contains four corners and four sides where opposite sides are of the same length and parallel to each other. The angles of a rectangle are equal in measure and are right-angled i.e. they measure 90°. Few real-life examples of a rectangle are dollar bills, a playing card, flat surface of a board, etc.
Properties of a Rectangle
Some of the properties of the rectangle are given below:
- Two pairs of parallel sides
- All four angles are right angles, that is, they measure 90 degrees.
- Opposite sides are of equal lengths
- Two equal diagonals
- In a rectangle, the two diagonals bisect each other in equal halves
In the rectangle PQRS, PQ II RS, PQ=RS, PS II QR, and PS=QR. All the angles are 90° angles.
A square is a kind of quadrilateral with all sides and angles with equal measure. The pair of opposite sides in a square are equal and parallel to each other along with angles measuring at 90°. A square is a flat-shaped figure that looks like a rectangle but is different in its properties. A real-life example of a square is a chessboard.
Properties of a Square
Some of the properties of the square are given below:
- Contains four vertices and four edges
- All the four internal angles measure 90°
- Diagonals are equal and perpendicular to each other
- All four sides and angles are equal
In the square PQRS, PQ = QR = RS = SP, the angles are at 90°, and PQ II RS and PS II QR.
A kite has various names such as a dart or an arrowhead because of the shape. A kite has two pairs of equal-length sides and these sides are adjacent to each other. A real-life example is a kite itself.
Properties of a Kite
Some of the properties of the kite are given below:
- Contains four edges and four vertices
- Contains one line of symmetry
- Contains two pairs of congruent and consecutive sides
- Diagonals are perpendicular to each other
In the kite PQRS, PQ = QR, and PS = SR.
Topics Related to Types of Quadrilaterals
Mentioned below are few topics that are related to the types of quadrilaterals. Click to know more!
Example 1: Cindy knows that the diagonals of a parallelogram bisect each other. If they bisect each other at 90°, does it become a rhombus?
Solution: Consider the parallelogram ABCD
In, Δ AEB and Δ AED
AE =AE (common), BE = ED (as diagonals of parallelogram bisect each other) and ∠AEB = ∠AED = 90° (given)
Therefore, by SAS Congruency, ΔAEB and ΔAED are congruent. So, AB = AD (by CPCT)
Similarly, considering Δ AED and Δ CED, AD = DC (using the same process). This further implies, AB=BC=CD=AD
We know that the sides of a rhombus are equal in length. Therefore, the given parallelogram is a rhombus.
Example 2: Can you find the angle x° in the following figure?
We know that the sum of the angles in a quadrilateral is 360°.
From the given figure, we get:
x +67 +77 + 101 =360°
x + 245 = 360°
Therefore, x° = 115°
Example 3: Identify the pairs of equal sides in the kite given below.
We know that a kite has two pairs of equal adjacent sides.
The pairs of adjacent sides in the above kite are (PQ, QR), (PQ, PS), (QR, RS), and (PS, RS)
Pairs of equal adjacent sides are (PQ, QR) and (PS, RS)
Therefore, the pairs of equal sides are (PQ, QR) and (PS, RS).
FAQs on Types of Quadrilaterals
What is Quadrilateral and its Types?
A polygon with four sides or edges and four corners or vertices is called a quadrilateral. The word is derived from two Latin words - Quadri and Latus, meaning four and sides respectively. A quadrilateral contains various properties such as a quadrilateral has four vertices and four sides along with four angles. In a quadrilateral, the sum of all four angles is equal to 360°. The lengths of the sides are different, and the angles are of different measures. However, some quadrilaterals have their sides and angles in equal measures. Based on the measurements of sides and angles, quadrilaterals can be classified as a parallelogram, rhombus, kite, square, rectangle, trapezium, and irregular quadrilaterals.
What are the Particular Types of Quadrilaterals?
There are six types of quadrilaterals, namely:
How many Types of Convex Quadrilaterals are there?
Quadrilaterals which have all four interior angle less than 180° are called convex quadrilaterals. There are various types of Convex Quadrilaterals such as:
Is a Parallelogram always a Quadrilateral?
Yes, a parallelogram is a quadrilateral but a quadrilateral is not always a parallelogram. A Quadrilateral is only a four-sided figure with no specific properties, whereas a parallelogram is a four-sided figure with opposite sides parallel and equal, opposite angles equal, and adjacent angles in a linear pair.
How many Types of Quadrilaterals do we have?
A quadrilateral refers to a four-sided polygon that has four angles. The seven types of quadrilaterals are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid. Quadrilaterals can also be classified as regular and irregular quadrilaterals and convex and concave quadrilaterals.
Why is a Rectangle not a Square?
A rectangle consists of four corners and four sides. The opposite sides are of the same length and parallel to each other. The angles of a rectangle are equal in measure and are right-angled i.e. they measure 90°. Whereas a square is the flattened version of a rectangle with different properties such as all sides and angles with equal measurements. The pair of opposite sides in a square are equal and parallel to each other along with angles measuring at 90°. Hence, a rectangle does not have all four sides of equal measure. This is the reason that a rectangle is not a square.