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Splash Screen. Five-Minute Check (over Lesson 5-4) Main Ideas California Standards Theorem 5.13: SAS Inequality/Hinge Theorem Example 1: Use SAS Inequality in a Proof Theorem 5.14: SSS Inequality Theorem Example 2: Prove Triangle Relationships Example 3: Relationships Between Two Triangles

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 5-4) Main Ideas California Standards Theorem 5.13: SAS Inequality/Hinge Theorem Example 1: Use SAS Inequality in a Proof Theorem 5.14: SSS Inequality Theorem Example 2: Prove Triangle Relationships Example 3: Relationships Between Two Triangles Example 4: Use Triangle Inequalities Lesson 5 Menu

  3. Do Now

  4. Do Now

  5. Apply the SAS Inequality. • Apply the SSS Inequality. Lesson 5 MI/Vocab

  6. Lesson 5 TH1

  7. Write a two-column proof. Given: Prove: Use SAS Inequality in a Proof Lesson 5 Ex1

  8. Proof: Statements Reasons 1. 1. Given 2. 2. Alternate interior angles are congruent. 3. Substitution 3. 4. 4. Subtraction Property 5. 5. Given 6. 6. Reflexive Property 7. 7. SAS Inequality Use SAS Inequality in a Proof Lesson 5 Ex1

  9. Lesson 5 TH2

  10. Given: Prove: Prove Triangle Relationships Lesson 5 Ex2

  11. Proof: Statements Reasons 1. 1. Given 2. 2. Reflexive Property 3. 3. Given 4. 4. Given 5. 5. Substitution 6. 6. SSS Inequality Prove Triangle Relationships Lesson 5 Ex2

  12. Relationships Between Two Triangles A. Write an inequality relating mLDM to mMDN using the information in the figure. Lesson 5 Ex3

  13. In ΔMDL and ΔMDN, The SSS Inequality allows us to conclude that Relationships Between Two Triangles Answer:mLDM > mMDN Lesson 5 Ex3

  14. By the SSS Inequality, Relationships Between Two Triangles B. Write an inequality finding the range of values containing a using the information in the figure. Lesson 5 Ex3

  15. Relationships Between Two Triangles SSS Inequality Substitution Subtract 15 from each side. Divide each side by 9. Also, recall that the measure of any angle is always greater than 0. Subtract 15 from each side. Divide each side by 9. Lesson 5 Ex3

  16. The two inequalities can be written as the compound inequality Relationships Between Two Triangles Lesson 5 Ex3

  17. Use Triangle Inequalities HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which foot can Nitan raise higher above the table? Assume both of Nitan’s legs have the same measurement, the SAS Inequality tells us that the height of the left foot opposite the 65° angle is higher than the height of his right foot opposite the 35° angle. This means that his left foot is raised higher. Answer: his left foot Lesson 5 Ex4

  18. Which reason correctly completes the two-column proof? Given:m1 < m3E is the midpoint of Prove:AC < AB Lesson 5 CYP1

  19. Proof: Statements 1. 2.3.4.5.6.7.8. Reasons 1.Given2.Definition of midpoint3.Reflexive Property4.Given5. Vertical Angle Theorem6.Definition of congruent angles7.Substitution8._______________ E is the midpointof 2  3 Lesson 5 CYP1

  20. A. SSS Inequality Theorem B. SAS Inequality Theorem C. Substitution D. none of the above • A • B • C • D Lesson 5 CYP1

  21. Which reason correctly completes the following proof? Given:X is the midpoint ofΔMCX is isosceles.CB > CM Prove: Lesson 5 CYP2

  22. Proof: Statements 1.2.3.4.5.6.7. Reasons 1.Given2.Definition of midpoint3.Given4.Definition of isosceles triangle5.Given6. Substitution7.______________ X is the midpoint of ΔMCX is isosceles. Lesson 5 CYP2

  23. A. SSS Inequality Theorem B. SAS Inequality Theorem C. Substitution D. none of the above • A • B • C • D Lesson 5 CYP2

  24. A. Compare mWYX and mZYW and write an inequality statement. • A • B • C • D A.mWYX < mZYW B.mWYX = mZYW C.mWYX > mZYW D.cannot be determined Lesson 5 CYP3

  25. A.6 < n < 12 B. C.n > 6 D.6 < n < 18.3 B. Find the range of values containing n and write an inequality statement. • A • B • C • D Lesson 5 CYP3

  26. HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Megan can lift her right foot 18 inches from the table and her left foot 13 inches from the table. Which leg makes the greater angle with the table? • A • B • C A. her right leg B. her left leg C. neither Lesson 5 CYP4

  27. End of Lesson 5

  28. Do Now

  29. Do Now

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