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5-5 Indirect Proofs

5-5 Indirect Proofs. Learning Goal: use indirect reasoning to find a contradiction. Notes: Indirect Reasoning. Indirect Reasoning considers all possibilities and proves all but one false. The one that remains must be true

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5-5 Indirect Proofs

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  1. 5-5 Indirect Proofs Learning Goal: use indirect reasoning to find a contradiction

  2. Notes: Indirect Reasoning • Indirect Reasoning considers all possibilities and proves all but one false. The one that remains must be true • “When you have eliminated the impossible, whatever remains, however improbable, must be the truth” ~ Sherlock Holmes

  3. Steps to Writing an Indirect Proof Step 1: Assume the opposite (negation) of what you want to prove. Step 2: Show that the negation leads to a contradiction. Step 3: Conclude that the assumption is false; therefore what you want to prove must be true.

  4. Writing the first statement Example: If you were writing an indirect proof for each statement, what would be the first thing you would assume? 1) You do not have soccer practice today. 2) Neither base is a right angle. 3) An integer is divisible by 5.

  5. Identifying the contradiction Example 2: Which 2 of the 3 statements contradict each other? a) ∆ABC is acute a) b) ∆ABC is scalene b) c) ∆ABC is equiangular c)

  6. EX 3: Indirect Proof • Given: 7(x + y) = 70 and • Prove: Step 1: y = 6 Step 2: Plug 6 in for y and look for contradiction Step 3:

  7. EX: Indirect Proof • Given:∆LMN is an equilateral triangle • Prove: none of the angles measure 900 Step 1: What do we assume? Step 2: Where is the contradiction?

  8. Got it? State the assumption and contradiction for this indirect proof. Given: Prove: AB is the longest side. C 80o 60o 400 B A

  9. Classwork Heading: 5-5 pg 339 # 3 – 9, 11, 13, 14, 16, 17 * For #17 just state the assumption and the contradiction (steps one and two) You have 15 minutes before I check your work.

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