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 |
| 4. | Parallelogram |
| 5. | Trapezium |
| 6. | Rhombus |
| 7. | Rectangle |
| 8. | Square |
| 9. | Kite |
| 10. | Solved Examples |
| 11. | Practice Questions |
| 12. | FAQs on Types 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:
In this section, let us discuss quadrilaterals' properties in general, which applies to all types of quadrilaterals. The properties of quadrilaterals are listed below:
Now, let us see the 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:
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:
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:
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:
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:
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:
In the kite PQRS, PQ = QR, and PS = SR.
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? Solution: 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°
x =115 Therefore, x° = 115°
Example 3: Identify the pairs of equal sides in the kite given below. Solution: 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).
