2. Inductive Reasoning
• Watching weather patterns
develop help forecasters…
• Predict weather..
• They recognize and…
• Describe patterns.
• They then try to make
accurate predictions based
on the patterns they
discover.
3. Patterns & Inductive Reasoning
• In Geometry, we will
• Study many
patterns…
• Some discovered by
others….
• Some we will
discover…
• And use those
patterns to make
accurate predictions
6. Using Inductive Reasoning
• Look for a Pattern
• (Looks at several
examples…use pictures
and tables to help
discover a pattern)
• Make a conjecture.
• (A conjecture is an
unproven “guess” based
on observation…it might
be right or
wrong…discuss it with
others…make a new
conjecture if necessary)
7. How do you know your
conjecture is True or False?
• To prove a conjecture is TRUE, you need
to prove it is ALWAYS true (not always
so easy!)
• To prove a conjecture is FALSE, you need
only provide a SINGLE counterexample.
• A counterexample is an example that
shows a conjecture is false.
8. Decide if this conjecture is
TRUE or FALSE.
• All people over 6 feet tall are good basketball
players.
• This conjecture is false (there are plenty of
counterexamples…)
• A full moon occurs every 29 or 30 days.
• This conjecture is true. The moon revolves
around Earth once approximately every 29.5
days.
13. Example
Describe the pattern and predict the next term
• 1, 4, 16, 64, …
The following number is four times the previous number.
(64)(4) = 256
• -5, -2, 4, 13, …
Add 3, then 6, then 9, so the next number would add 12.
13 + 12 = 25
14. Using Inductive Reasoning
1. Look for a Pattern- look at several
examples. Use diagrams and tables to
help find a pattern.
2. Make a Conjecture- (an unproven
statement that is based on
observations)
3. Verify the Conjecture- Use logical
reasoning to verify the conjecture. It
must be true in all cases.
15. Counterexamples
• A counterexample is an example that
shows that a conjecture is false.
• Not all conjectures have been proven true
or false. These conjectures are called
unproven or undecided.