Download INDUCTIVE REASONING AND CONJECTURE

INDUCTIVE REASONING
AND CONJECTURE
DEFINITIONS
•
Conjecture: a best guess based on known information.
•
Inductive Reasoning: using specific examples to arrive
at a generalization or prediction.
•
Counterexample: an example that demonstrates that a
conjecture is not true.
EXAMPLES
2
1
EXAMPLES
PRACTICE
• Pg.
64 #11-20, 29-36
CONDITIONAL
STATEMENTS
DEFINITIONS
•
Conditional statement: a statement that can be written
in if-then form.
•
If-then statement: written in the form "if p, then q"
• If I study, then I will get good
grades
•
Hypothesis: the "if" part. "If I study"
•
Conclusion: the "then" part. "Then I will get good
grades"
DEFINITIONS
•
Related conditionals: other statements based on a
conditional statement
• If it is raining, then there are clouds in the
sky
• Converse: if there are clouds in the sky, then it is
raining.
• Inverse: if it is not raining, then there are no clouds in
the sky.
•
Contrapositive: if there are no clouds in the sky, then it
is not raining
•
The original statement and the contrapositive are
always logically equivalent.
EXAMPLES
Hypothesis
Hypothesis
Hypothesis
Conclusion
Conclusion
Conclusion
EXAMPLES
Tru
e
Tru
e
Fals
e
EXAMPLES
•
Write the converse, inverse, and contrapositive of the
following statement:
If there is a lot of snow, then school is cancelled.
Converse: If school is cancelled, then there is a lot of
snow.
Inverse: If there is not a lot of snow,then school is not
cancelled.
Contrapositive: If school is not cancelled, then there is
not a lot of snow.
PRACTICE
Pg. 78 #16-27, 34-39
POSTULATES AND
PARAGRAPH PROOFS
VOCABULARY
•
Postulate (or Axiom): A statement that describes a
fundamental relationship between the basic terms of
Geometry. It is accepted as true.
•
Theorem: a statement that can be proven true.
•
Proof: a logical argument in which each statement is
supported by a postulate, theorem, or logic.
•
Paragraph Proof: an informal proof to prove that a
conjecture is true.
•
2.1--Through any two points, there is exactly one line
•
2.2--Through any three points not on the same line,
there is exactly one plane
•
2.3--A line contains at least 2 points.
•
2.4--A plane contains at least 3 non-collinear points.
•
2.5--If 2 points are in a plane, then the line containing
those points are also in the same plane.
•
2.6--If 2 lines intersect, they intersect at exactly one
point.
•
2.7--If 2 planes intersect, they intersect at exactly one
line.
POSTULATES
EXAMPLE
Never
Sometime
s
Sometime
s
Always
Always
Sometime
s
PRACTICE
Pg. 92 #16-27
ALGEBRAIC PROOF
PROPERTIES
EXAMPLE
Simplif
y
Simplif
y
Simplif
y
EXAMPLE
PRACTICE
Pg. 97 #14-25
PROVING SEGMENT
RELATIONSHIPS
POSTULATE
EXAMPLE
Substitution
PRACTICE
PG. 104 #12-21
ANGLE RELATIONSHIPS
POSTULATES
THEOREMS
EXAMPLES
EXAMPLES
PRACTICE
PG. 112 #16-24, 27-32