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A TEXT BOOK OF MATHEMATICS CLASS IX

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Page 1: DIGITAL TEXT BOOK

A TEXT BOOK OF

MATHEMATICSCLASS IX

MATHEMATICS

Class IX

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1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

6.

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

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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

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.:. 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

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= 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

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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

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.:. 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

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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

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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

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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

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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

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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

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A TEXT BOOK OF

MATHEMATICSCLASS IX

MATHEMATICS

Class IX