similars

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Similarity Similarity Similarity Similarity Similarity

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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

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

Similar Figures: 

Similar Figures Two figures are similar if they have the same shape but not necessary the same size. Similar figures Non-similar figures Continue

The following are similar figures.: 

The following are similar figures. I II

The following are similar figures.: 

III IV V Back to Similar Figures The following are similar figures.

The following are non-similar figures.: 

The following are non-similar figures. I II

The following are non-similar figures.: 

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

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

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

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

Similar Triangles: 

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

Similar Triangles: 

Two triangles are similar if pairs of corresponding sides are proportional. SSS Property Next page Similar Triangles

Similar Triangles: 

Two triangles are similar if 2 pairs of sides are proportional and their included angles are congruent. Next page Similar Triangles A  X SAS Property

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I II The following are non-similar triangles Next page

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III IV Next page

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1. Which of the following is similar to the above triangle?

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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

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3. Are the following triangles similar ? A. Yes B. No Which similarity property do you have to check?

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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. Name the similar triangles and give reasons. 3. Are the following triangles similar ?

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4. Are the following triangles similar ? A. Yes B. No

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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. 4. Are the following triangles similar ?

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5. Are the following triangles similar ? A. Yes B. No A.S.S. is not a property of similarity

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6. Are the following triangles similar? What are the two triangles? A. Yes B. No A AHK and ACB

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

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

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

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

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9. In the figure, the two triangles are similar. What are c and d ? A. c = 8.5 , d = 3 B. c = 8.5 , d = 6 C. c = 8 , d = 6 D. c = 8 , d = 3

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10. In the figure, the two triangles are similar. What are x , y and 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

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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