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A TEXT BOOK OF
MATHEMATICSCLASS IX
MATHEMATICS
Class IX
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Ploygon
CONTENT
Chapter 1
Polygon
Examples of Polygon
Exterior angles
Sum of Angles
Regular Polygon
Chapter 2 RATIONAL NUMBERS
Rational Numbers
Rational forms
Addition and subtraction
Multiplication and Division
Equal Rationals
Decimal forms
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 of the angles of a triangle is 1800
Polygons 1
.:. Sum of the angles of Quadrilateral is 2 x 1800
Sum of the angles of Pentagon 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 of sides = 10
Sum of the angles = (10 - 2) x 1800
Polygons 2
= 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 of the four angles of the quadrilateral is 360°
So, the sum of the four external angle is
720° - 360° = 360°
.:. The Sum of the external angles
= n x 1800-[(n-2) x 180°]
= 2x 180°
= 360°
The sum of external angles of any polygon is 360°.
Polygons 3
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 of the polygon are equal. Its external angles will also be equal.
Sum of the interior angle = 360° 3600
So the measure of an external = ---yo = 36°
Polygons 4
.:. 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 of the external angles = 3600
3600
Measure of an external angle = 36 = 10
Measure of an internal angle = 1800 - 10
= 1700
Polygons 5
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
Example
2x x ---2y y
.:. If ~ and p are two rational numbers. Then sum of
the rationalq 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 of the rational number is
a p aq-bp = ~-----''-b q bq
Example
x y y x
Rational Numbers 7
xy
.:. If ~ and : are two rational numbers.
Then multiplication of the 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 of this 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
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
221 So 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
4x+2y _ 4x+3x 7x
5x-2y 5x-3x 2x
7 =
2
Decimal Forms
Decimal forms express fractions as sums of powers
of _1 10
Example
~ = 0.222 9
Rational Numbers 10
A TEXT BOOK OF
MATHEMATICSCLASS IX
MATHEMATICS
Class IX