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Splash Screen. Five-Minute Check (over Lesson 5-2) Main Ideas and Vocabulary California Standards Key Concept: Writing an Indirect Proof Example 1: State Assumptions Example 2: Algebraic Proof Example 3: Real-World Example Example 4: Geometry Proof. Lesson 3 Menu. Do Now. Do Now.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 5-2) Main Ideas and Vocabulary California Standards Key Concept: Writing an Indirect Proof Example 1: State Assumptions Example 2: Algebraic Proof Example 3: Real-World Example Example 4: Geometry Proof Lesson 3 Menu

  3. Do Now

  4. Do Now

  5. Use indirect proof with algebra. • Use indirect proof with geometry. • indirect reasoning • indirect proof • proof by contradiction Lesson 3 MI/Vocab

  6. Lesson 3 KC1

  7. A. B. C. D. • A • B • C • D Lesson 3 CYP1

  8. A. B. C. D. • A • B • C • D Lesson 3 CYP1

  9. PLH. A. B.MLH  PLH C. D. • A • B • C • D Lesson 3 CYP1

  10. Given: Write an indirect proof in the correct order. Prove: Part BAssume that Part A The assumption leads to a contradiction. Therefore, the assumption that must be false, which means that must be true. Indirect Proof: Lesson 3 CYP2

  11. Part C Substitute –3 for a in the inequality Substitution Multiply. Add. This is a contradiction because the denominator cannot be 0. Lesson 3 CYP2

  12. A. C, B, A B. C, A, B C. B, C, A D. B, A, C • A • B • C • D Lesson 3 CYP2

  13. Given: David spent less than $135. Prove: At least one of the sweaters x cost less than $32. That is, SHOPPING David bought four new sweaters for a little under $135. The tax was $7, but the sweater costs varied. Show that at least one of the sweaters cost less than $32. Which is the correct order for this indirect proof? Lesson 3 CYP3

  14. Indirect Proof: Part B Assume that none of the sweaters cost less than $32. Part A then the minimum total amount David spent is However, this is a contradiction since David spent less than $135. Part C The assumption leads to a contradiction of a known fact. Therefore, the assumption that must be false. Thus, at least one of the sweaters cost less than $32. Lesson 3 CYP3

  15. A. A, C, B B. B, A, C C. B, C, A D. C, B, A • A • B • C • D Lesson 3 CYP3

  16. Which is the correct order for this indirect proof? Given:ΔABCwith side lengths 8, 10, and 12 as shown. Prove:mC > mA Lesson 3 CYP4

  17. Indirect Proof: Part A Assume that Part CBy angle-side relationships, By substitution, This inequality is a false statement. Part B Since the assumption leads to a contradiction, the assumption must be false. Therefore, mC > mA. Lesson 3 CYP4

  18. A. C, B, A B. C, A, B C. B, A, C D. A, C, B • A • B • C • D Lesson 3 CYP4

  19. End of Lesson 3

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