Digital text book

1. A TEXT BOOK OF
MATHEMATICS
CLASS IX
MATHEMATICS
Class IX

14. 1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
6.
Ploygon
CONTENT
Chapter 1
Polygon
Examples of Polygon
Exterior angles
Sum ofAngles
Regular Polygon
Chapter 2
RATIONAL NUMBERS
Rational Numbers
Rational forms
Addition and subtraction
Multiplication and Division
Equal Rationals
Decimal forms

15. Chapter I
POLYGONS
.:. A polygon is a figuare having morethan three sides
and angles.
Examples of Polygons
.:. Divide any polygon into another polygon with one
side less and a triangle by drawing a line starting at
any vertex, skipping one vertex and joining with
the next
.:. Sum ofthe angles of a triangle is 1800
Polygons
1

16. .:. Sum ofthe angles of Quadrilateral is 2 x 1800
Sum of the angles ofPentagon is 3 x 1800
The sum of the angles of an n sides polygon is (n-2) x
1800
Example
A 10 sided polygon has all its angles equal. How
much is each angle?
Number ofsides = 10
Sum ofthe angles = (10 - 2) x 1800
Polygons 2

17. = 1440°
Since the angles are equal in measure the measure of an
angle = 1440
10
= 144°
Exterior Angles
[
.:. The four external angles and the four angles of the
quadrilateral together make
4 x 180° = 720°
The sum ofthe four angles ofthe quadrilateral is 360°
So, the sum ofthe four external angle is
720° - 360° = 360°
.:. The Sum ofthe external angles
= n x 1800
-[(n-2) x 180°]
= 2x 180°
= 360°
The sum of external angles of any polygon is 360°.
Polygons 3

18. Example
The angles of a triangle are 30°, 40° and 110°0 Find
the measures of its external angles.
Let's assume the exterior angles are x,y,Z
So external angles
Example
x = 180° - 30 = 150
y= 180° - 40 = 140
Z = 180° - 110 = 700
A 10 sided polygon has all its angles equal. How much is
each external angle?
Since the angles ofthe polygon are equal. Its exter-
nal angles will also be equal.
Sum of the interior angle = 360°
3600
So the measure of an external = ---yo
= 36°
Polygons 4

19. .:. Regular Polygon
polygon with equal angles and equal sides are called
regular polygon.
Example
How much is an internal angle of a 36 sided regular
polygon?
Sum ofthe external angles = 3600
3600
Measure of an external angle = 36
= 10
Measure of an internal angle = 1800
- 10
= 1700
Polygons 5

20. Chapter 2
RATIONAL NUMBERS
Rational Number
Integers and fractions are collectively called rational
numbers.
Any rational number can be written in the formx ,
where x and yare integers. Y
Example
1 2 3- - - - -
* 2 4 6
3 6 9
-=-=-
* 5 10 15
.:. If the numerator and denominator of a rational
number has any common factor then by removing
this factor, get a simpler form of the same rational
number.
Rational Numbers 6

21. Example
2x x
---
2y y
.:. If ~ and p are two rational numbers. Then sum of
the rational
q
number is
Example
a p aq bp
-+-=-+-
b q bq bq
_ aq+bp
bq
a p .
If b and ~are two ratIOnal numbers.
Then subtraction ofthe rational number is
a p aq-bp
=~-----''-
b q bq
Example
x y
y x
Rational Numbers 7

22. xy
.:. If ~ and : are two rational numbers.
Then multiplication ofthe rational number is
Example
a p ap
- x-=-
b q bq
2 5 2x5
- x -=--
3 7 3x7
10
=
21
a p
.:. If band qare two rational numbers. Then division
ofthis rational number is
a p a q aq
- +-=- x-=-
b q b p bp
for the numbers a,b,p,q if a = p then aq = bp
b q
f!:...=p
If aq = bp and also b "* 0, q "* °then b q
Rational Numbers 8

23. Example
187 221
Whether 209 and 247 are equal?
Check whether the product of 187 x 247 and
209 x 221 are equal
187 x 247 = 46189
209 x 221 = 46189
221So 187
, 209 and 247 are equal
a p a b
For the numbers a,b,p,q if - = -then - =-
b q p q
Example
x 2 4x+2y
- =-what is
y 3 5x-2y
x 2
-=-
y 3
3x=2y
Rational Numbers 9

24. 4x+2y _ 4x+3x 7x
5x-2y 5x-3x 2x
7
=
2
Decimal Forms
Decimal forms express fractions as sums ofpowers
of _1
10
Example
~ = 0.222
9
Rational Numbers 10

25. A TEXT BOOK OF
MATHEMATICS
CLASS IX
MATHEMATICS
Class IX