1. Similarity Similarity Similarity Similarity Similarity Similarity

2. Cat mother, MiMi, lost her daughters, would you please help her to find her daughters. Her daughters have the similar footprint with their mother.
MiMi’s footprint

3. Contents 1. Introduction to Similar Figures
2. Introduction to Similar Triangles
3. Exercises on Similar Triangles
4. Summary of Similar Triangles

4. Similar Figures
Two figures are similar if they have the same shape but not necessary the same size.
Similar figures
Non-similar figures
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5. The following are similar figures.II

6. The following are similar figures.
III
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Similar Figures IV V

7. The following are non-similar figures.II

8. The following are non-similar figures.
III
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Similar Figures IV V

9. Now can you find MiMi’s daughters?
MiMi’s footprint

10. Consider Dr. Evil and Mini Me from Austin Powers
Consider Dr. Evil and Mini Me from Austin Powers. Mini Me is supposed to be an exact replica of Dr. Evil

11. Similar Triangles
Two triangles are similar if pairs of corresponding angles are congruent. A X
Next page Z Y C B
A  X, B  Y, A  Z ABC ~ XYZ
AA Property

12. Similar Triangles SSS Property
Two triangles are similar if pairs of corresponding sides are proportional. X Z Y A B C
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SSS Property

13. Similar Triangles
Two triangles are similar if 2 pairs of sides are proportional and their included angles are congruent. X Y Z A B C
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A  X SAS Property

14. The following are non-similar trianglesII
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15. III
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16. Which of the following is similar to the above triangle?1.
Which of the following is similar to the above triangle? A B C

17. 2. Give the reason for why the following triangles are similar?
A. 3 angles congruent
B. 3 sides proportional
C. 2 sides proportional and included angle

18. 3. Are the following triangles similar ?B C 7 6 8 L 4 N M
3.5 3
A. Yes
B. No
Which similarity property do you have to check?

19. 3. Are the following triangles similar ?B C 7 6 8 L 4 N M
3.5 3
Name the similar triangles and give reasons.
A. ABC ~  LNM by S.S.S.
B. ABC ~ MLN by S.S.S.
C. ABC ~ LNM by A.A.
D. ABC ~ MLN by A.A.

20. 4. Are the following triangles similar ?
47º A B C
47º
A. Yes
B. No

21. 4. Are the following triangles similar ?
47º A B C
47º
Name the similar triangles and give reasons.
A. ABC ~ LMN by S.S.S.
B. ABC ~ MNL A.A.
C. ABC ~ MNL by S.S.S.
D. ABC ~ NLM A.A.

22. A.S.S. is not a property of similarity
5. Are the following triangles similar ? P R Q
46º
3.5 4 A B C
46º 8 7
A. Yes
B. No
A.S.S. is not a property of similarity

23. 6. Are the following triangles similar? What are the two triangles?
51º H B K C
A. Yes
B. No
AHK and ACB

24. 6. The triangles are similar ?
Name the triangles and give reasons. A
51º H B K C
A.  AHK ~  ABC by A.A.
B.  AHK ~  ACB by A.A.
C.  AHK ~  ACB by S.A.S.
D.  AHK ~  BAC by S.A.S.

25. 7. Are the following triangles similar ?
35º
A. Yes
B. No

26. 7. Name the similar triangles and give the reason.
35º A B C D E
A.  ABC ~  CDE by A.A.
B.  ABC ~  EDC by A.A.
C.  ABC ~  CDE by S.A.S.
D.  ABC ~  EDC by S.A.S.

27. 8. In the figure, the two triangles are similar.
What are x and y ? P A 7 y x 6 C Q 3 R 8 B
A. x = 4, y = 3.5
B. x = 3.5, y = 6
C. x = 3.5, y = 4
D. x = 4, y = 5

28. 9. In the figure, the two triangles are similar.
What are c and d ? A B C P Q R 10 6 c 5 4 d
A. c = 8.5 , d = 3
B. c = 8.5 , d = 6
C. c = 8 , d = 6
D. c = 8 , d = 3

29. 10. In the figure, the two triangles are similar.
What are x , y and z ? A B C P Q R 6 8 3 x y z
A. x = 10 , y = 4 , z = 5
B. x = 10 , y = 4 , z = 20
C. x = 10 , y = 16 , z = 5
D. x = 10 , y = 16 , z = 20

30. 3 Conditions of Similar Triangles :
SUMMARY
3 Conditions of Similar Triangles :
1. 3 pairs of angles congruent
2. 3 pairs of sides proportional
3. 2 sides proportional and included congruent angles