Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.

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Presentation transcript:

Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning. Geometry 3.0 – Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.

Deductive Reasoning – (Logical Reasoning) is the process of reasoning logically from given statements to a conclusion. Inductive Reasoning – is reasoning that is based on patterns you observe. 384, 192, 96, 48, … Given: If  A is acute, m  A < 90. Then we can say that  A is acute.

If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle. The Law of Syllogism: If p  q and q  r are true, then p  r is a true statement. So you can conclude: If a quadrilateral is a square, then it is a rectangle.

A Counterexample to a statement is a particular example or instance of the statement that makes the statement false. Any perfect square is divisible by is a perfect square and Counterexample – 25 is a perfect square and isn’t divisible by 2.