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Geometry Section 5-5 1112
- 1. Section 5-5 The Triangle Inequality Thursday, March 15, 2012
- 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. Exercise Draw a triangle with the following side lengths: 6 cm, 4 cm, and 10 cm Thursday, March 15, 2012
- 4. Theorem 5.11 - Triangle Inequality Theorem Thursday, March 15, 2012
- 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 side Thursday, March 15, 2012
- 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 2 Thursday, March 15, 2012
- 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 2 Thursday, March 15, 2012
- 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 2 Thursday, March 15, 2012
- 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 > 7.2 Thursday, March 15, 2012
- 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. 13 Thursday, March 15, 2012
- 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. 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 Thursday, March 15, 2012
- 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 12.4 Thursday, March 15, 2012
- 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 AC Thursday, March 15, 2012
- 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. 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. 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. Check Your Understanding Look at #1-5 on page 362 Thursday, March 15, 2012
- 19. Problem Set Thursday, March 15, 2012
- 20. Problem Set p. 363 #7-33 odd, 43, 53, 57 "If you can find a path with no obstacles, it probably doesn't lead anywhere." - Frank A. Clark Thursday, March 15, 2012