Transcript Slide 1

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.
Given:
If A is acute, mA < 90.
Then we can say that A is acute.
Inductive Reasoning – is reasoning that is based
on patterns you observe.
384, 192, 96, 48, …
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
isn’t divisible by 2.