2.4 Deductive Reasoning2.5 Postulates

Geometry R/H

Students will be able to distinguish between Inductive and Deductive

Reasoning, and to determine the validity of a conjecture.

Deductive Reasoning To review, when you make a conclusion

based on a pattern of observations, you are applying inductive reasoning.

We also know how to show that a conditional is false – find a counterexample. But how do we show that a conditional is true?

We must use deductive reasoning. Deductive reasoning is the process of using

logic to draw conclusions from given facts, definitions and properties.

Is the conclusion a result of inductive or deductive reasoning?

Example 1: Media Application

There is a myth that you can balance an egg on its end only on the spring equinox. A person was able to balance an egg on July 8, September 21, and December 19. Therefore this myth is false.

Since the conclusion is based on a pattern of observations, it is a result of inductive reasoning.

Check It Out! Example 2 There is a myth that an eelskin wallet will demagnetize credit cards because the skin of the electric eels used to make the wallet holds an electric charge. However, eelskin products are not made from electric eels. Therefore, the myth cannot be true. Is this conclusion a result of inductive or deductive reasoning?

The conclusion is based on logical reasoning from scientific research, so it is a result of deductive reasoning.

Applying Deductive Reasoning

See if you can draw a correct conclusion from the following information.

Given: If a team wins 10 games, then they play in the finals. If a team plays in the finals, then they travel to Boston. The Ravens won 10 games.

Conclusion: The ravens will travel to Boston.

Inductive or Deductive Reasoning

1. By observing many individual cases, people concluded that malaria was caused by breathing air in swampy areas.

2. All students must study Algebra I before studying Geometry. Mia is studying Geometry. Therefore, Mia has studied Algebra I

3. Any quadrilateral with four congruent angles is a rectangle. A square has four congruent angles. A square is a rectangle.

4. I see that every time it rains Sally has an umbrella. I saw Sally with an umbrella on Tuesday. Therefore it must rain on Tuesday.

Summary:

Is the conclusion a result of inductive or deductive reasoning?

1. At Colonia High School, students must pass Geometry before they can take Algebra 2. Emily is in Algebra 2, so she must have passed Geometry.

Valid Conclusions

When a conclusion is based on logical reasoning and facts then we say the conclusion is valid.

If the reasoning is not logical, then the conclusion is not valid.

Look at the following conclusions to see if they are valid or not.

Summary:Determine if each conjecture is valid?2. Given: If a person is able to vote in a U.S.

election, they must be at least 18 years old. Joe is 18 years old.

Conjecture: Joe voted in the last election.

3. Given: Two angles that are congruent have the same measure. The measures of two vertical angles are the same.

Conjecture: The two vertical angles must be congruent.

MORE DEDUCTIVE REASONING EXAMPLES

Look to Word Document

FHSFHS Unit BUnit B 1111

2.5 Vocabulary

• postulate

• axiom

• proof

• theorem

Concept

Concept

Example 1Analyze Statements Using Postulates

A. Determine whether the following statement is always, sometimes, or never true. Explain.

If plane T contains contains point G, then plane T contains point G.

Example 2Analyze Statements Using Postulates

B. Determine whether the following statement is always, sometimes, or never true. Explain.

contains three noncollinear points.

Example 3

A. Determine whether the statement is always, sometimes, or never true.

Plane A and plane B intersect in exactly one point.

A. always

B. sometimes

C. never

Example 2B. Determine whether the statement is always, sometimes, or never true.

Point N lies in plane X and point R lies in plane Z. You can draw only one line that contains both points N and R.

A. always

B. sometimes

C. never

Concept

Concept

Homework

Deductive versus Inductive Reasoning Worksheet

Book Work for Section 2.5 Pg. 130 #1-9 odd, 10-13 all, 17-29

odd, 34-40 even