Chapter 1 Tools of Geometry

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Chapter 1Tools of Geometry

• Sec 1 1
• Patterns and Inductive Reasoning

Objectives 1) To use inductive reasonings to
make conjectures.
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• Inductive Reasoning Is reasoning that is based
  on patterns you observe.
• If you observe a pattern in a sequence you can
  use inductive reasoning to find the next term.
• Ex. 1 Find the next term in the sequence
• A) 3, 6, 12, 24, ___, ___
• B) 1, 2, 4, 7, 11, 16, 22, ___, ___
• C)

48
96
Rule x2
29
37
Rule 1, 2, 3, 4,
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• Inductive Reasoning assumes that an observed
  pattern will continue. This may or may not be
  true.
• Ex x x x
• This is true only for x 0 and x 1
• Conjecture A conclusion you reach using
  inductive reasoning.

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• Ex. 2 Make a conjecture about the sum of the
  first 30 odd numbers.

12 22 32 42 52 302
1 1 1 3 4 1 3 5 9 1 3 5
7 16 1 3 5 7 9 25 1 3 5
... 30
900
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To show that a conjecture is always true, you
must prove it.
To show that a conjecture is false, you have to
find only one example in which the conjecture is
not true. This case is called a counterexample.
A counterexample can be a drawing, a statement,
or a number.
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• Counter Example To a conjecture is an example
  for which the conjecture is incorrect.
• Ex.1-3 The first 3 odd prime numbers are 3, 5,
  7. Make a conjecture about the 4th.
• 3, 5, 7, ___
• One would think that the rule is add 2, but that
  gives us 9 for the fourth prime number.
• Is that true?
• What is the next odd prime number?

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GEOMETRY LESSON 1-1
Each year the price increased by 1.50.
A possible conjecture is that the price in 2003
will increase by 1.50.
If so, the price in 2003 would be 11.00 1.50
12.50.
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Homework

• Page 6
• 1-53 odd and 2,26,40,44,48

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GEOMETRY LESSON 1-1
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GEOMETRY LESSON 1-1
31. 31, 43 32. 10, 13 33. 0.0001,
0.00001 34. 201, 202 35. 63, 127 36. ,
37. J, S 38. CA, CO 39. B, C
28. and is improper.
29. 75F 30. 40 push-ups answers may vary.
Sample Not very confident, Dino may reach
a limit to the number of push-ups he can do
in his allotted time for exercises.
1 2
1 3
3 2
3 2
22. The sum of the first 100 odd numbers is
1002, or 10,000. 23. 555,555,555 24. 123,454,32
1 2528. Answers may vary. Samples are
given. 25. 8 (5 3) and 3 gt 8 26. gt
and gt 27. 6 (4) lt 6 and 6
(4) lt 4
31 32
63 64
/
1 3
1 3
1 2
1 2
1 3
1 2
/
/
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GEOMETRY LESSON 1-1
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GEOMETRY LESSON 1-1
50. His conjecture is probably false because
most peoples growth slows by 18 until they
stop growing somewhere between 18 and 22
years. 51. a. b. H and I c. a circle
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GEOMETRY LESSON 1-1
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GEOMETRY LESSON 1-1