This document is a textbook on mathematics for class 9. It contains summaries of two chapters: polygons and rational numbers. The polygons chapter defines polygons, gives examples, and discusses properties such as the sum of interior angles and exterior angles. It also defines regular polygons. The rational numbers chapter defines rational numbers as integers and fractions, and discusses how to add, subtract, multiply, and divide rational numbers. It also covers converting between fractional and decimal forms of rational numbers.

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