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, mA < 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 2.

Counterexample – 25 is a perfect square and 25 is a perfect square and isn’t divisible by 2. isn’t divisible by 2.