 # similars

Published on January 23, 2008

Author: Regina1

Source: authorstream.com

Slide1:  Similarity Similarity Similarity Similarity Similarity Slide2:  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 Slide3:  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. Slide9:  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 Slide14:  I II The following are non-similar triangles Next page Slide15:  III IV Next page Slide16:  1. Which of the following is similar to the above triangle? Slide17:  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 Slide18:  3. Are the following triangles similar ? A. Yes B. No Which similarity property do you have to check? Slide19:  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 ? Slide20:  4. Are the following triangles similar ? A. Yes B. No Slide21:  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 ? Slide22:  5. Are the following triangles similar ? A. Yes B. No A.S.S. is not a property of similarity Slide23:  6. Are the following triangles similar? What are the two triangles? A. Yes B. No A AHK and ACB Slide24:  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. Slide25:  7. Are the following triangles similar ? A. Yes B. No Slide26:  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. Slide27:  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 Slide28:  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 Slide29:  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 Slide30:  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

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