Download 2.1 (Inductive Reasoning and Conjecture).notebook

2.1 (Inductive Reasoning and Conjecture).notebook
February 11, 2013
Conjecture­an educated guess based on known information.
Conjectures are Always, Sometimes or Never True.
Section 2.1
Always, Sometimes or Never
How do you know if something is always, sometimes or never true?
ALWAYS ­ you can state the rule (aka theorem) that makes it TRUE
e.g ­ An angle bisector cuts an angle into two congruent angles. (Angle Bisector Theorem).
SOMETIMES ­ If you can find one example of a conjecture being true and one where it isn't, then it is SOMETIMES TRUE.
NEVER ­ If you can state a rule that shows it is never true, then a conjecture is never true.
Example #1
Make a conjecture about the next number based on
the pattern, then find the next 3 numbers.
-8, -5, -2, 1, 4.
Pattern is
Conjectures are a result of one of two different types of Reasoning.
Deductive Reasoning ­ reasoning that uses a set of rules to make a conclusion.
e.g. ­ A midpoint cuts a segment into two congruent segments. B is the midpoint of segment AC. Conjecture: AB = BC.
Inductive Reasoning­reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction.
e.g. ­ By measuring the angles of two angles formed by an angle bisector, in four different examples, the two angles are congruent. So the conjecture is that the angle bisector cuts the angles in to two congruent angles.
Example #2
Determine if the following conjecture is always,
sometimes, or never true based on the given
information
Given: Collinear points D, E, and F
Conjecture: DE + EF = DF
Answer: Sometimes ­ if E is not between D and F, then it is not true, but it E does fall between D and F, then it is true. SO SOMETIMES IT's TRUE. Next 3 numbers: 7, ____, _____
True
E
F
D
This is my example.
False
D
E
F
This is my counter example.
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2.1 (Inductive Reasoning and Conjecture).notebook
Information: BD is an angle bisector of <ABC
Make a conjecture about the given information.
Draw a figure to illustrate the conjecture.
February 11, 2013
Determine whether the conjecture is true or false.
Give a counter example for any false conjecture.
Given: DE= EF
Conjecture: E is the midpoint of DF
Conjecture:
p. 64-65 #22-36 even
2/14/13
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