1. SIMILARITY

2. WHAT IS SIMILARITY????
Similarity is the name given to two figures having the same shape, but different sizes. In simpler words, one figure is an enlargement of the other.
Similarity is the quality of being similar. It refers to the closeness of appearance between two or more objects. It is the relation of sharing properties

3. DEFINITIONS
Corresponding - similar especially in position or purpose; equivalent
Ratio - the relationship between two numbers or quantities (usually expressed as a quotient)
Proportion - the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree
Congruent - equilateral, equal, exactly the same (size, shape, etc.)
Enlargement - expansion: the act of increasing (something) in size or volume or quantity or scope
Theorem - an idea accepted as a demonstrable truth
Scale factor – reduced ratio of corresponding sides of two similar figures.

4. EXAMPLES
THESE TWO SHAPES ARE SIMILAR

5. 1. Corresponding angles are equal
Two polygons are said to be similar if and only if there is a one-to-one correspondence between their vertices such that:
1. Corresponding angles are equal
2. Lengths of corresponding sides are in proportion.
EXAMPLE: W X Y Z
4 cm
2 cm B C A D
2 cm
1 cm

6. TRIANGLES

7. CONDITIONS FOR SIMILAR TRIANGLES
Side angle side (SAS)
40° W Y X
6 cm
8 cm A B C
3 cm
4 cm
If a pair of corresponding sides of two triangles are in the same proportion and the angle between the sides are equal, then the triangles are similar.

8. Angle angle side triangle (AAS)
If the corresponding angles of two triangles are equal, then the two triangles are similar. Y X Z A B C

9. . side side side triangles (SSS)
In this type of similarities, the triangles are similar when three sides of the triangle are corespnding. So, ‘if all pairs of corresponding sides of two triangles are proportional, then triangles are similar.
NOTE : In side side side triangles, their corresponding sides are manified by a certain factor ,K. W X Y
6 cm
8 cm
12 cm
6 cm
3 cm
4 cm A B C

10. THE FIGURES WHICH ARE ALWAYS SIMILAR!!!

11. Circles
Regular Pentagons
Squares
Equilateral Triangles

12. AREAS OF SIMILAR FIGURES
The following rectangles are similar and their ratio of corresponding sides is y. ABCD is of length b and width a.
If two figures are similar and their sides are in the ratio y, then their areas will be in the ratio y2”. Yb Z Y X W ya A a b D B C

13. SIMILARITY IN 3 DIMENSIONAL FIGURES

14. SIMILAR 3-D FIGURES IN OUR DAILY LIVES

15. Thus, the corresponding sides should be in the same ratio.
When solid objects are similar, one is an accurate enlargement of the other.
Thus, the corresponding sides should be in the same ratio.
140 cm
84 cm
100 cm
60 cm
80 cm
48 cm

16. VOLUMES AND SURFACE AREAS OF SIMILAR 3-D OBJECTS
A and B are two similar 3-D shapes. Their ratio of corresponding sides is .
If the ratio of the corresponding
sides of two 3-D objects is k,
then the ratio of their surface areas is B ka kb kc A a b c

17. B ka kb kc A a b c
If the ratio of the corresponding sides of two 3-D objects is k, then the ratio of their volumes is

18. When solid objects are similar, one is an accurate enlargement of the other. If two objects are similar and the ratio of corresponding sides (scale factor) is k, then the ratio of their volumes is k3.
A line has one dimension, and the scale factor is used once.
An area has two dimensions, and the scale factor is used twice.
A surface area of 3 dimensional figures also uses the scale factor twice.
A volume has three dimensions, and the scale factor is used three times. S U M A R Y

19. QUESTIONS
Ravina looks in a mirror and sees the top of a building. His eyes are 1.25 m above ground level, as shown in the following diagram.
If Ravina is 1.5 m from the mirror and m from the base of the building, how high is the building?

20. Solution to problem
So, the height of the building is 150 m.

21. QUESTION

22. ANSWER
P= 7.2
Q= 6.4

23. QUESTION

24. SOLUTION

25. QUESTION
Two similar spheres made of the same material have weights of 32kg and 108 kg respectively. If the radius of the larger sphere is 9cm, find the radius of the smaller sphere.

26. SOLUTION
We may take the ratio of weights to be the same as the ratio of volumes.
Ratio of volumes (k3) = =
Ratio of corresponding lengths (k) =
 Radius of smaller sphere = × 9
= 6cm

27. Bibliography
The information in this presentation were taken from the projects submitted by our class on the topic of similarity. ©

28. BY: Suhail Lalji Fatema Sharrif Masoomali Fatehkia Ravina Pattni
WE HOPE THAT THE PRESENTATION WAS GOOD AND INFORMATIVE.
THANK YOU
BY:
Suhail Lalji
Fatema Sharrif
Masoomali Fatehkia
Ravina Pattni
Mohammed Jaffer