This presentation is Created by ….Ms Rashmi Kathuria at…

Our Aim is to learn the concept Of similarity in mathematics.

Contents

• Introduction of the topic.

• Examples

• Similarity in mathematics

Introduction :

There are variety of objects aroundyou. Some of these have same shapebut not necessarily the same size.

What do you call them?

Want to know?

We call them..

DAILY LIFE AND SIMILARITY

Observe the leaves and petals of a flower .

Observe the feathers of two or moresame birds.

SIMILAR OBJECTS

They have same shape but not necessarily the same size

Observe these cats.

They are similar.

Similarity & Mathematics

Figures that have same shape butnot necessarily the same size are called similar figures.

PLEASE NOTE

ANY TWO LINE SEGMENTS ARE SIMILAR.

A B

C DANY TWO CIRCLES ARE SIMILAR.

PLEASE NOTEANY TWO SQUARES ARE SIMILAR.

A B

CD

E F

GH

ANY TWO EQUILATERALTRIANGLES ARE SIMILAR.

A B

CD E

F

DEFINITION TWO POLYGONS ARE SAIDTO BE SIMILAR TO EACHOTHER ,IF

1.their correspondingangles are equal.

2.the lenghts of theircorresponding sidesare proportional.

Example:

A

B

C

D

E

F

G

H

Quad. ABCD is SIMILAR TO Quad. EFGHB = F

C = G

D =H

ALSO AB/EF = BC/FG = CD/GH = DA/HE.

How to write ?F a polygon ABCDEF is similarto a polygon GHIJKL , then wewrite

Poly ABCDEF ~ Poly GHIJKL

Note: ~ stands for “is similar to”.

Checking for Similarity

Square and Rectangle.

Consider a square ABCD

A B

CDand a rectangle PQRS.

P Q

RThey are equiangular but their

sides are not proportional.

They are not similar.

S

Checking for Similarity

Two Hexagons.

Consider a hexagon ABCDEF

and another hexagon GHIJKL.

They are equiangular, but their

sides are not proportional. They are not similar.

A

B C

D

EF

G

H I

J

KL

Checking for Similarity

Two Quadrilaterals.

Consider a quadrilateral ABCD

A B

CDand another quadrilateral PQRS.

P Q

RSThey have their corresponding sides proportional but their corresponding angles are not equal.

They are not similar.

Checking for Similarity

Two Equilateral Triangles.

Consider an equilateral triangle ABC

A B

C

and another equilateral triangle PQR.

P Q

R

They have their corresponding sides proportional . Also their corresponding angles are equal.

They are similar.

If one polygon is similar to a second polygon and

~the second polygon is similarto the third polygon, then ~

the first polygon is similar to the third polygon. ~

I hope you have clearly understoodthe concept of similarity in daily lifeand in mathematics.