Similarity

This is a presentation to explain the concept of similarity in mathematics.

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

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

3. Contents
•Introduction of the topic.
•Examples
•Similarity in mathematics

4. Introduction :
There are variety of objects around
you. Some of these have same shape
but not necessarily the same size.
What do you call them?
Want to know?

5. We call them..

6. DAILY LIFE AND SIMILARITY
Observe the leaves and petals of
a flower .
Observe the feathers of two or more
same birds.

7. SIMILAR OBJECTS
They have same shape
but not necessarily
the same size

8. Observe these cats.
They are similar.

9. Similarity & Mathematics
Figures that have same shape but
not necessarily the same size are
called similar figures.

10. PLEASE NOTE
ANY TWO LINE SEGMENTS ARE
SIMILAR.
A B
C D
ANY TWO CIRCLES ARE
SIMILAR.

11. PLEASE NOTE
ANY TWO SQUARES ARE
SIMILAR.
A B
CD
E F
GH
ANY TWO EQUILATERAL
TRIANGLES ARE SIMILAR.
A B
C
D E
F

12. DEFINITION
TWO POLYGONS ARE SAID
TO BE SIMILAR TO EACH
OTHER ,IF
1.their corresponding
angles are equal.
2.the lenghts of their
corresponding sides
are proportional.

13. Example:
A
B
C
D
E
F
G
H

Quad. ABCD
is SIMILAR TOQuad. EFGH
B = F
C = G
D =H
ALSO
AB/EF = BC/FG
= CD/GH = DA/HE.

14. How to write ?
F a polygon ABCDEF is similar
to a polygon GHIJKL , then we
write
Poly ABCDEF ~ Poly GHIJKL
Note: ~ stands for
“is similar to”.

15. Checking for Similarity
Square and Rectangle.
Consider a square ABCD
A B
CD
and a rectangle PQRS.
P Q
R
They are equiangular but their
sides are not proportional.
They are not similar.
S

16. 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

17. Checking for Similarity
Two Quadrilaterals.
Consider a quadrilateral ABCD
A B
CD
and another quadrilateral PQRS.
P Q
R
S
They have their corresponding sides
proportional but their corresponding
angles are not equal.
They are not similar.

18. 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.

19. If one polygon is similar
to a second polygon and
~
the second polygon is similar
to the third polygon, then ~
the first polygon is similar
to the third polygon. ~

20. I hope you have clearly understood
the concept of similarity in daily life
and in mathematics.