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Lesson 7.5 Triangle Inequality pp. 287-290

Lesson 7.5 Triangle Inequality pp. 287-290. Objectives: 1. To state and prove the triangle inequality. 2. To apply the triangle inequality to triangle existence problems and to problem-solving strategies. A. A. 15. 12. 9. 7. 5. A. 3. B. 8. C. B. 8. C. B. 8. C.

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Lesson 7.5 Triangle Inequality pp. 287-290

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  1. Lesson 7.5 Triangle Inequality pp. 287-290

  2. Objectives: 1. To state and prove the triangle inequality. 2. To apply the triangle inequality to triangle existence problems and to problem-solving strategies.

  3. A A 15 12 9 7 5 A 3 B 8 C B 8 C B 8 C

  4. Definition A point M isBetweenA and B if AM + MB = AB. The correct notation is A-M-B.

  5. Theorem 7.14 Triangle Inequality. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  6. 2 3 ? 7

  7. EXAMPLEIn a business office the equipment must be arranged carefully for efficient use. Becky uses primarily the computer on her desk, the photocopier, and the fax machine. A triangular arrangement is desired to facilitate access between all three machines. The distance between her desk and the photocopier must be the shortest, and the total distance between the three items should not exceed 20 feet.

  8. Comp.-CopierCopier-faxComp.-Fax 1. 5 ft 7 ft 6 ft 2. 3 ft 6 ft 9 ft

  9. Practice: Can a triangle be constructed with segments of length 5, 8, and 13? 1. Yes 2. No

  10. Practice: Can a triangle be constructed with segments of length 4, 6, and 1? 1. Yes 2. No

  11. Practice: Given two sides of a triangle equal 4 and 7, what is the range of possible values for the third side? 3  x  11 The third side must be greater than the difference but less than the sum.

  12. Practice: Given two sides of a triangle equal 9 and 18, which of the following is a possible length for the third side? 1. 9 2. 28 3. 12 4. 8

  13. Homework pp. 289-290

  14. a b c 1. 5 9 10 3. 8 4 12 5. 6 3 3 ►A. Exercises State whether triangles with the following side lengths exist. If not, state the reason.

  15. ►A. Exercises AB, BC, and AC are given. Make a sketch and identify the type of triangle. If none is formed, explain why (impossible, collinear). 7. AB = 3, BC = 5, AC = 2

  16. ►A. Exercises AB, BC, and AC are given. Make a sketch and identify the type of triangle. If none is formed, explain why (impossible, collinear). 9. AB = 5, BC = 3, AC = 1

  17. ►A. Exercises AB, BC, and AC are given. Make a sketch and identify the type of triangle. If none is formed, explain why (impossible, collinear). 11. AB = 5, BC = 3, AC = 3

  18. ►B. Exercises Refer to Becky’s office in the example in this section. Are the following measurements possible? If not, explain why. Computer-Copier Copier-Fax Computer-Fax 13. 5 feet 7 feet 8 feet 15. 6 feet 12 feet 10 feet 17. 5 feet 9 feet 6 feet

  19. ■ Cumulative Review Supply the missing reasons needed to complete the following proof. Given: AD  AB, CB  CD Prove: D  B A C x D B

  20. STATEMENTS REASONS 22. ADAB; CBCD 22. 23. A and C are 23. right angles 24. A  C 24. 25. AXD  CXD 25. 26. D  B 26. Given Def. of Perp. All rt. ’s are  Vert.  Thm. Third ’s 

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