2'1 Inductive Reasoning and Conjecture 10608

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2.1 Inductive Reasoning and Conjecture 10/6/08

• A conjecture an educated guess based on known
  information.
• Examining several specific situations to come to
  a conjecture is known as inductive reasoning.
• Inductive reasoning is reasoning that uses a
  number of examples to arrive at a plausible
  generalization or prediction.

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Patterns and Conjecture

• 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.

1
3
6
10
15
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Patterns and Conjecture

• The numbers represented below are called
  triangular numbers. Make a conjecture about the
  next triangular number based on the pattern.
• Find a pattern
• 1 3 6 10 15
• Conjecture the next number will increase by 6.
  So the next number will be 15 6 21.

1
3
6
10
15
3
2
4
5
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Geometric Conjecture

• For points P, Q, and R, PQ 9, QR 15, and PR
  12. Make a conjecture and draw a figure to
  illustrate your conjecture.
• Given points P, Q, and R, PQ 9, QR 15, and
  PR 12
• Examine the measures of the segments.
• Since PQ QR ? PR, the points cannot be
  collinear.
• Conjecture P, Q, and R are not collinear.

Q
15
9
P
R
12
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Find Counterexamples

• A conjecture based on several observations may be
  true in most circumstances, but false in others.
• It takes only one false example to show that a
  conjecture is not true. The false example is
  called a counterexample.

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Find Counterexamples

• Find a counterexample for the following statement
  based on the graph.
• The mortgage rates for March decreased from
  February.
• Examine the graph.
• The statement is true for a 15-year mortgage and
  a 5-year adjustable rate mortgage.
• However the rates for a 30-year mortgage remained
  the same from February to March. The statement is
  false for a 30-year mortgage.
• So, the 30-year mortgage is a counterexample to
  the statement.

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Extra Practice!!!

• Classwork - Study Guide 2.1.
• Homework RTL 2.1
• PSAT Practice Chapter 1