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Inductive Reasoning and Conjecture

Inductive Reasoning and Conjecture. Unit 2 2/3/11. A Conjecture is a guess based on analyzing information or observing a pattern. Inductive Reasoning is to make a conjecture after looking at several situations. (An educated guess).

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Inductive Reasoning and Conjecture

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  1. Inductive Reasoning and Conjecture Unit 2 2/3/11

  2. A Conjecture is a guess based on analyzing information or observing a pattern. • Inductive Reasoning is to make a conjecture after looking at several situations. (An educated guess).

  3. Make a conjecture about the next number in the following sequence… 1, 3, 9, 27, 81,… What is the pattern? Conjecture: the next number will be 243.

  4. Find the pattern and make a conjecture about the next number in the sequence. • -5, 10, -20, 40… • 1, 10, 100, 1000…

  5. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. • <1 and <2 form a right angle. Draw a picture: Conjecture: <1 and <2 are complementary angles.

  6. <ABC and <DBE are vertical angles. Draw a picture: Conjecture: m<ABC = m<DBE

  7. Finding Counterexamples • A Counterexample is a false example. • A conjecture is false if there is even one situation in which the conjecture is not true. • A counterexample can be a written explanation or simply a picture.

  8. Determine whether the conjecture is true or false. If false, give a counterexample. • Given’s are set in stone. They are FACT. • Conjectures are simply guesses!! Ex. Given: AB = BC Conjecture: B is the midpoint of AC. Draw a picture: Counterexample? Is the conjecture True or False?

  9. Given: Points A, B, and C are collinear. • Conjecture: AB + BC = AC Draw a Picture: Counterexample? Is the conjecture True or False?

  10. Given: <R and <S are supplementary. <R and <T are supplementary. • Conjecture: <T and <S are congruent. Draw a Picture: Counterexample? Is the conjecture True or False?

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