Pre-AP Geometry Name: Worksheet 1.7: Inductive Reasoning ...
Geometry 1.1 patterns and inductive reasoning
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Transcript of Geometry 1.1 patterns and inductive reasoning
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1.1 Patterns and Inductive Reasoning
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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.
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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
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Visual Patterns
• Can you predict and sketch the next figure in these patterns?
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Number Patterns
• Describe a pattern in the number sequence and predict the next number.
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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)
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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.
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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.
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Sketch the next figure in the pattern….
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How many squares are in the next figure?
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PatternsSketch the next figure in the pattern.
321 4
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Patterns
5
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ExampleDescribe the pattern and predict the next term
• 1, 4, 16, 64, …
• -5, -2, 4, 13, …
The following number is four times the previous number.
(64)(4) = 256
Add 3, then 6, then 9, so the next number would add 12.
13 + 12 = 25
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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.
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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.