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Chapter 5 Section 5 Indirect Proof

Chapter 5 Section 5 Indirect Proof. Objectives. Students will be able to use indirect reasoning to write proofs. Essential Undersanding. You can use indirect reasoning as another way to write proofs. What is Indirect Reasoning?.

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Chapter 5 Section 5 Indirect Proof

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  1. Chapter 5 Section 5Indirect Proof

  2. Objectives Students will be able to use indirect reasoning to write proofs

  3. Essential Undersanding You can use indirect reasoning as another way to write proofs

  4. What is Indirect Reasoning? All possibilities are considered and then all but one possibility is proved false and the remaining possibility must be true

  5. Indirect Proofs • Also known as proof by contradiction • To write an indirect proof: • you state the negation of what you want to prove • Show the negation leads to a contradiction (false statement) • Conclude that the temporary assumption must be false and that what you want to prove must be true

  6. Writing the First Step: The Negation of the Statement Write the negation of the statement and assume temporarily that it is true An integer x is divisible by 3 Negation: Assume an integer x is not divisible by 3 You do not have soccer practice today ΔBOX is not acute At least one pair of shoes you bought cost more than $25

  7. Identifying Contradictions Another important step in writing indirect proofs is to be able to recognize when you have a contradiction In general you want to arrive at a contradiction of the given statement of your proof

  8. Identifying Contradictions What two statements are a contradiction of each other? I) FG || KL II) FG ≅ KL III) FG perp. KL I)ΔABC is scalene II)ΔABC is equilateral III)ΔABC is not scalene I)ΔABC is acuteII)ΔABC is scaleneIII)ΔABC is equiangular

  9. Writing an Indirect Proof Usually written in a paragraph or bulleted format Write an Indirect Proof Given: ΔABC is scalene Prove: <A, <B, and <C all different measures Step 1 write the negation Step 2 show a contradiction Step 3 conclude the temporary assumption is false and the prove statement is true

  10. Writing an Indirect Proof Write an Indirect Proof Given: 7(x + y) = 70, x ≠ 4 Prove: y ≠ 6 Step 1 write the negation Step 2 show a contradiction Step 3 conclude the temporary assumption is false and the prove statement is true

  11. Homework Pg. 319 # 4 – 15, 22 13 problems

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