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Chapter 2 Section 1     Miss Novak
Conjecture• An educated guess based   on known information.
Inductive     Reasoning  • Reasoning that uses anumber of specific examples   to arrive at a plausiblegeneralization or pr...
Patterns andConjectures
Give it a try!• The numbers represented below are called  triangular numbers. Make a conjecture about  the next triangular...
Find a Pattern: 1+2=3 3+3=6 6+4=10So the numbers increase by 2, 3 and 4.
Counter Example• An example used to show that a given statement is not always true.
Find a Counter Example1. Given: DE = EF   Conjecture: E is the midpoint of DF   Answer: True, there is no counter example.
Find a Counter Example2. Given: JK = KL = LM = MJ   Conjecture: JKLM forms a square  Answer: JKLM may not have all right a...
Find a Counter Example3. Given: n is a real number   Conjecture: n x n is nonnegative number  Answer: True, there is no co...
As you can see you cannot alwaysfind a counter example, but when      you do they prove the   conjecture/statement false.
HomeworkChapter 2 Section 1#1-17 odd#29-37 odd
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Chapter 2 section 1

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Transcript of "Chapter 2 section 1"

  1. 1. Chapter 2 Section 1 Miss Novak
  2. 2. Conjecture• An educated guess based on known information.
  3. 3. Inductive Reasoning • Reasoning that uses anumber of specific examples to arrive at a plausiblegeneralization or prediction
  4. 4. Patterns andConjectures
  5. 5. Give it a try!• The numbers represented below are called triangular numbers. Make a conjecture about the next triangular number based on the pattern.Observe: Each triangle is formed by adding another row of dots.
  6. 6. Find a Pattern: 1+2=3 3+3=6 6+4=10So the numbers increase by 2, 3 and 4.
  7. 7. Counter Example• An example used to show that a given statement is not always true.
  8. 8. Find a Counter Example1. Given: DE = EF Conjecture: E is the midpoint of DF Answer: True, there is no counter example.
  9. 9. Find a Counter Example2. Given: JK = KL = LM = MJ Conjecture: JKLM forms a square Answer: JKLM may not have all right angles.
  10. 10. Find a Counter Example3. Given: n is a real number Conjecture: n x n is nonnegative number Answer: True, there is no counter example.
  11. 11. As you can see you cannot alwaysfind a counter example, but when you do they prove the conjecture/statement false.
  12. 12. HomeworkChapter 2 Section 1#1-17 odd#29-37 odd
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