Warm Up:

Work in your teams to sort the following conditional statements (there are 4 different statements)

2.2 Inductive and Deductive Reasoning

Use logic to consider the validity of conditional statements

Inductive reasoning is used to make Conjectures

A Conjecture can be proven false with a Counter Example

Inductive reasoning: When you find a pattern in specific cases and then write a conjecture for the general case.

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Conjectures: an unproven statement that is based on observations ...I’ve got a hunch based on these observations

Counter example: a conjecture must be true for all cases, to prove it wrong, find one example that does not work

Using inductive reasoning, make a conjecture about what the next figure will look like...

1)

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2)

Make and test a conjecture about:

The sign (positive or negative) of the product of any three negative integers.

Provide a counterexample to the following statement to prove the statement invalid.

If line k intersects BE, then line k is a segment bisector.

Deductive Reasoning vs. Inductive Reasoning

Uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

Uses specific examples and patterns to form a conjecture about something in general.

Laws of Logic for Deductive Reasoning:

These laws can be valid or invalid!

Law of Detachment: In a conditional statement: If the hypothesis is true, then the conclusion is also true.

Law of Syllogism: Cutting out the middleman.

If a→ b and b→ c, then we can say a→ c

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Using deductive reasoning, what statement can you make given the following?

What Law of Logic did you just use?

“If two segments are the same length, then they are congruent, BC=FG.”

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Using deductive reasoning, what statement can you make given the following?

Valid or Invalid?

Valid or Invalid?

If you ace all of your geometry tests, then you will get an A in your math class. If you get an A in your math class, you will pass geometry.

If it is your birthday, your grandma gives you $20. You get $20.