Types of Quadrilaterals

Types of quadrilaterals are discussed here:

In a quadrilateral family, each member has four sides, four vertices and four angles.

Types of Quadrilaterals

1. Rectangle:

A rectangle is a parallelogram in which all the angles are right angles.

Here ABCD is a rectangle.

Rectangle

(i) So, AB is parallel to DC.

AD is parallel to BC.

(ii) AD = BC

   AB = DC

(iii) ∠A = ∠B = ∠C = ∠D = 90°

Definition of Rectangle:

A parallelogram having each angle a right angle is called a rectangle.


Definition of Rectangle

In the figure, ABCD is a rectangle, in which AB || DC, AD || BC, AB = CD, AD = BC and diagonal AC = diagonal BD and all angles are right angles.


2. Square:

A square is a rectangle in which all sides are equal.

Here ABCD is a square.

Square

(i) AB is parallel to DC.

BC is parallel to AD.


(ii) AB = BC = CD = DA.

(iii) ∠A = ∠B = ∠C = ∠D = 90°


Definition of Square:

A parallelogram having all sides equal and all angles of right angles is called a square.

Definition of Square

In the figure, ABCD is a square, in which AB || DC, AD || BC, AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D =90°.


3. Trapezium:

A quadrilateral is called trapezium if a pair of its opposite sides are parallel.

Here ABCD is a trapezium.

Trapezium

AB is parallel to DC.


Definition of Trapezium:

A quadrilateral having one pair of parallel sides is called trapezium. Other pair of opposite sides may or may not be parallel.

Definition of Trapezium

In the above figure, ABCD is a trapezium, in which AB ||DC


Note:

If a trapezium has non parallel sides equal, it is called isosceles trapezium.

Isosceles Trapezium

An isosceles trapezium is a quadrilateral having exactly one pair of parallel sides and the non-parallel sides are of equal length. i.e., AB || CD and AD = BC


4. Parallelogram:

A quadrilateral whose opposite sides are parallel and equal is called a parallelogram. Its opposite angles are equal.

Here LMNO is a parallelogram.

Parallelogram

(i) LM is parallel to ON.

LO is parallel to MN.

(ii) LO = MN

     LM = ON

(iii) ∠L = ∠N

     ∠M = ∠O


Definition of Parallelogram:

A quadrilateral having both pairs of opposite sides parallel is called a parallelogram.

Definition of Parallelogram

In the figure, ABCD is a parallelogram, in which AB || DC and AD || BC.


Note: All parallelogram are trapezium but all trapezium are not parallelogram.


5. Rhombus:

A rhombus is a parallelogram whose all sides are equal, opposite sides are parallel and opposite angles are equal.

Here LMNO is a rhombus.

Rhombus

(i) LM = MN = NO = OL

(ii) ∠L = ∠N

    ∠O = ∠M


(iii) LM is parallel to ON

OL is parallel to MN


Definition of Rhombus:

A parallelogram having all sides equal is called a rhombus.

Definition of Rhombus

In the figure, ABCD is a rhombus, in which AB || DC, AD || BC and AB = BC = DC = DA

Let’s discuss about the properties of types of quadrilateral in the table below;

Types of Quadrilaterals

Comparing the sides and angles of the different quadrilateral are discussed above.

Identifying Features of Quadrilaterals:

Name of Quadrilateral

Identifying Features

Figures

1. Rectangle

A parallelogram with all angles right angles.

Identifying Features of Rectangle


2. Square


A rhombus with all angles right angles.

Identifying Features of Square


3. Rhombus


A parallelogram with all sides equal.

Identifying Features of Rhombus


4. Parallelogram


A quadrilateral having 2 pairs of opposite sides parallel and equal.

Identifying Features of Parallelogram


5. Kite


A quadrilateral having 2 pairs of adjacent sides equal.

Identifying Features of Kite

6. Trapezium

A quadrilateral having 1 pair of opposite sides parallel.

Identifying Features of Trapezium

7. Isosceles Trapezium

A trapezium with a pair of non-parallel opposite sides equal.

Identifying Features of Isosceles Trapezium
Identifying Features of Quadrilaterals

Questions and Answers on Types of Quadrilaterals:

1. From the figures given below, state which of the following are quadrilaterals?

Quadrilaterals Question

Solution:

(i) No, it is a triangle containing 3 sides.

(ii) Yes, it is a quadrilateral with 4 sides.

(iii) No, is a hexagon with 6 sides.

(iv) Yes, it is a quadrilateral with 4 sides.


Quadrilaterals Questions

2. From the adjoining figure, state whether the following statements are true or false: 

(i) AB = DC

(ii) AB||BC

(iii) ∠BAD = ∠BCD

(iv) ∠ABC=∠DAB

Solution:

(i) True, since AB and DC are opposite sides of parallelogram ABCD.

(ii) False, since AB and BC are adjacent sides of parallelogram ABCD.

(iii) True, since ∠BAD and ∠BCD are opposite angles of parallelogram ABCD.

(iv) False, since ∠ABC and ∠DAB are adjacent angles of parallelogram ABCD.


3. How many rectangles can be found in the following figure? Name them.

Quadrilateral Rectangle Question

Solution:

9 rectangles; ABCD, AGHD, GBCH, AEFB, EDCF, AGIE, GBFI, IFCH, IHDE

You might like these

● Quadrilaterals.

Elements of a Quadrilateral.

Types of Quadrilaterals.

Parallel Lines.

Perpendicular Lines.

Construction of Perpendicular Lines by using a Protractor.

Sum of Angles of a Quadrilateral.

Worksheet on Quadrilateral.

Practice Test on Quadrilaterals.






5th Grade Geometry Page

5th Grade Math Problems

From Types of Quadrilaterals to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  2. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  3. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  4. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  5. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More