physicscatalyst.com logo







Understanding Quadrilaterals


In this page we will explain the topics for the chapter 3 of Understanding Quadrilaterals Class 8 Maths.We have given quality notes and video to explain various things so that students can benefits from it and learn maths in a fun and easy manner, Hope you like them and do not forget to like , social share and comment at the end of the page.

What is Closed curve and Open curve

Closed curve is a figure in the plane with no end points. It completely encloses an area
 
Closed curve and Open curve
 
 
Open curve is a figure in the place with end points
 

 

What are polygons

A simple closed curve made up of only line segments is called a polygon.

 
Understanding Quadrilaterals notes Class 8

Classification of polygons

 
We classify polygons according to the number of sides( or vertices)
Number of sides
Classification
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
 

Diagonal in Polygons

A diagonal is a line segment connecting two non-consecutive vertices of a polygon
Understanding Quadrilaterals notes Class 8  
 
 

Convex and Concave Polygons

Convex Polygon
We have all the diagonals inside the Polygon
Understanding Quadrilaterals notes Class 8
 
Concave Polygon
We don’t have all the diagonals inside the Polygon
Understanding Quadrilaterals notes Class 8
We will be concentrating on Convex Polygon in this chapter

Regular and Irregular Polygons

A regular polygon is both ‘equiangular’ and ‘equilateral’.
So all the sides and angles should be same
a) So square is a regular polygon but rectangle is not
b) Equilateral triangle is a regular polygon

Angle Sum in the Polygons

The Sum of the angles in the polygon is given by
=(n-2) × 1800
For Triangle, n=3
So Total =1800
For quadrilateral, n=4
So total =3600
 
Example
Find the value of angle x

Solution
We know in the quadrilateral, sum of interior angle is 3600
So
50+130+120+x=360
x=600
Watch this tutorial on how to solve angle problems in quadrilateral

Sum of the Measures of the Exterior Angles of a Polygon

The sum of the measures of the external angles of any polygon is 360°.
This property is very useful is finding number of sides of the polygons

Example:
Find the number of sides of a regular polygon whose each exterior angle
has a measure of 60°.
Solution: Total measure of all exterior angles = 360°
Measure of each exterior angle = 60°
Therefore, the number of exterior angles =360/60=6
The polygon has 6 sides.
Watch this tutorial on how to solve exterior angles problems

What is Quadrilaterals

A quadrilateral is a four sides Polygon. It has four angles
 
Understanding Quadrilaterals notes Class 8
 
Angle Sum Property
Sum of angles of the Quadrilaterals =3600
Exterior Angle Property
Sum of exterior angles of the Quadrilaterals =3600

Types of Quadrilaterals

 

Trapezium


Trapezium is a quadrilateral with a pair of parallel sides.
Understanding Quadrilaterals notes Class 8
 

Isosceles trapezium


Trapezium when non-parallel sides of it are of equal length
 

Kite


It is a quadrilaterals having exactly two distinct consecutive pairs of sides of equal length
Here ABCD is a Kite

AB=BC
AD=CD
 

Parallelogram


It is a quadrilateral whose opposite sides are parallel.

Here ABCD is a Parallelogram
AD || BC, AB ||CD
Property 1
The opposite sides of a parallelogram are of equal length.
AD=BC , AB=CD
Property 2
The opposite angles of a parallelogram are of equal measure
∠A= ∠C , ∠B= ∠D
Property 3
The adjacent angles in a parallelogram are supplementary.
∠A+ ∠D=180 , ∠B+ ∠C=180
Property 4
The diagonals of a parallelogram bisect each other

Example
Understanding Quadrilaterals notes Class 8
Find the value of the angles x,y,z in the parallelograms given above
Solution
Angle B and Angle D are opposite angle and are equal
So y=1000
Angle C and Angle B are adjacent angle and are supplementary
So x+100=180
x=800
Angle A and Angle C are opposite angle and are equal
So z=800

Rhombus


A rhombus is a quadrilateral with sides of equal length
A rhombus has all the properties of a parallelogram and also that of a kite.
 
 
Special Property
The diagonals of a rhombus are perpendicular bisectors of one another

Rectangle


A rectangle is a parallelogram with equal angles
 
Property 1
Each angle is of 900
Property 2
The diagonals of a rectangle are of equal length

Square


A square is a rectangle with equal sides.
So it has the same property of Rectangle in addition of 4 equal sides

Property
The diagonals of a square are perpendicular bisectors of each other.
 
Watch this tutorial for understanding quadrilaterals


 

Go Back to Class 8 Maths Home page Go Back to Class 8 Science Home page