Geometry Section 5-5 1112

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The Triangle Ineq

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Geometry Section 5-5 1112

  1. 1. Section 5-5 The Triangle InequalityThursday, March 15, 2012
  2. 2. Essential Questions • How do you use the Triangle Inequality Theorem to identify possible triangles? • How do you prove triangle relationships using the Triangle Inequality Theorem?Thursday, March 15, 2012
  3. 3. Exercise Draw a triangle with the following side lengths: 6 cm, 4 cm, and 10 cmThursday, March 15, 2012
  4. 4. Theorem 5.11 - Triangle Inequality TheoremThursday, March 15, 2012
  5. 5. Theorem 5.11 - Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle must be greater than the length of the third sideThursday, March 15, 2012
  6. 6. Example 1 Is it possible to form a triangle with the given side lengths? If not, explain why not. 1 1 1 a. 6 , 6 ,14 b. 6.8, 7.2, 5.1 2 2 2Thursday, March 15, 2012
  7. 7. Example 1 Is it possible to form a triangle with the given side lengths? If not, explain why not. 1 1 1 a. 6 , 6 ,14 b. 6.8, 7.2, 5.1 2 2 2 1 1 1 No; 6 + 6 <14 2 2 2Thursday, March 15, 2012
  8. 8. Example 1 Is it possible to form a triangle with the given side lengths? If not, explain why not. 1 1 1 a. 6 , 6 ,14 b. 6.8, 7.2, 5.1 2 2 2 Yes 1 1 1 No; 6 + 6 <14 2 2 2Thursday, March 15, 2012
  9. 9. Example 1 Is it possible to form a triangle with the given side lengths? If not, explain why not. 1 1 1 a. 6 , 6 ,14 b. 6.8, 7.2, 5.1 2 2 2 Yes 1 1 1 No; 6 + 6 <14 2 2 2 5.1 + 6.8 > 7.2Thursday, March 15, 2012
  10. 10. Example 2 In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following measures cannot be AC? Why not? a. 7 b. 9 c. 11 d. 13Thursday, March 15, 2012
  11. 11. Example 2 In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following measures cannot be AC? Why not? a. 7 b. 9 c. 11 d. 13 7.2 + 5.2 =Thursday, March 15, 2012
  12. 12. Example 2 In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following measures cannot be AC? Why not? a. 7 b. 9 c. 11 d. 13 7.2 + 5.2 = 12.4Thursday, March 15, 2012
  13. 13. Example 2 In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following measures cannot be AC? Why not? a. 7 b. 9 c. 11 d. 13 7.2 + 5.2 = 12.4 So the third side must be less than 12.4Thursday, March 15, 2012
  14. 14. Example 2 In ∆ABC, AB = 7.2 and BC = 5.2. Which of the following measures cannot be AC? Why not? a. 7 b. 9 c. 11 d. 13 7.2 + 5.2 = 12.4 So the third side must be less than 12.4 d. 13 cannot be a measure for ACThursday, March 15, 2012
  15. 15. Example 3 The towns of Mitarnowskia, Fuzzy-Jeffington, and Sheckyville are shown in the map below. Prove that by driving from Mitarnowskia to Fuzzy-Jeffington and then Fuzzy-Jeffington to Sheckyville is a greater distance than driving from Mitarnowskia to Sheckyville.Thursday, March 15, 2012
  16. 16. Example 3 The towns of Mitarnowskia, Fuzzy-Jeffington, and Sheckyville are shown in the map below. Prove that by driving from Mitarnowskia to Fuzzy-Jeffington and then Fuzzy-Jeffington to Sheckyville is a greater distance than driving from Mitarnowskia to Sheckyville. Let the vertices be F, M, and S.Thursday, March 15, 2012
  17. 17. Example 3 The towns of Mitarnowskia, Fuzzy-Jeffington, and Sheckyville are shown in the map below. Prove that by driving from Mitarnowskia to Fuzzy-Jeffington and then Fuzzy-Jeffington to Sheckyville is a greater distance than driving from Mitarnowskia to Sheckyville. Let the vertices be F, M, and S. By the Triangle Inequality Theorem, MF + FS > MS.Thursday, March 15, 2012
  18. 18. Check Your Understanding Look at #1-5 on page 362Thursday, March 15, 2012
  19. 19. Problem SetThursday, March 15, 2012
  20. 20. Problem Set p. 363 #7-33 odd, 43, 53, 57 "If you can find a path with no obstacles, it probably doesnt lead anywhere." - Frank A. ClarkThursday, March 15, 2012

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