geometry section 2-4 1112

Section 2-4

Deductive Reasoning

Thursday, November 6, 14

Essential Questions

How do you use the Law of Detachment?

How do you use the Law of Syllogism?


Vocabulary

1. Deductive Reasoning:

2. Valid:

3. Law of Detachment:


Vocabulary

1. Deductive Reasoning: Using facts, rules, definitions, and properties to reach a logical conclusion from given statements

2. Valid:



Vocabulary


2. Valid: A logically correct statement or argument



Vocabulary



3. Law of Detachment: If p q is a true statement and p is true, then q is true.


Vocabulary



3. Law of Detachment: If p q is a true statement and p is true, then q is true.Example: Given: If a computer has no battery, then it won’t turn on.Statement: Matt’s computer has no battery.Conclusion: Matt’s computer won’t turn on.


Vocabulary

4. Law of Syllogism:


Vocabulary

4. Law of Syllogism: If p q and q r are true statements, then p r is a true statement


Vocabulary

4. Law of Syllogism:

Example: Given: If you buy a ticket, then you can get in the arena. If you get in the arena, then you can watch the game.Conclusion: If you buy a ticket, then you can watch the game.

If p q and q r are true statements, then p r is a true statement


Example 1

Determine whether each conclusion is based on inductive or deductive reasoning. Explain your

choice.a. In Matt Mitarnowski’s town, the month of March

had the most rain for the past 6 years. He thinks March will have the most rain again this year.


Example 1


choice.a. In Matt Mitarnowski’s town, the month of March

had the most rain for the past 6 years. He thinks March will have the most rain again this year.

This is inductive reasoning, as it is using past observations to come to the conclusion.


Example 1


choice.

b. Maggie Brann learned that if it is cloudy at night it will not be as cold in the morning than if there are

no clouds at night. Maggie knows it will be cloudy tonight, so she believes it will not be cold tomorrow.


Example 1


choice.

b. Maggie Brann learned that if it is cloudy at night it will not be as cold in the morning than if there are

no clouds at night. Maggie knows it will be cloudy tonight, so she believes it will not be cold tomorrow.

This is deductive reasoning, as Maggie is using learned information and facts to reach the

conclusion.


Example 2

Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain

your reasoning.

Given: If a figure is a right triangle, then it has two acute angles.

Statement: A figure has two acute angles.Conclusion: The figure is a right triangle.


Example 2


your reasoning.

Given: If a figure is a right triangle, then it has two acute angles.

Statement: A figure has two acute angles.Conclusion: The figure is a right triangle.

Invalid conclusion. A quadrilateral can have two acute angles, but it is not a right triangle.


Example 3


your reasoning with a Venn diagram.

Given: If a figure is a square, it is also a rectangle.Statement: The figure is a square.

Conclusion: The square is also a rectangle.


Example 3





A square has four right angles and opposite parallel sides, so

it is also a rectangle


Example 3





Rectangles

Squares

A square has four right angles and opposite parallel sides, so

it is also a rectangle


Example 4

Draw a valid conclusion from the given statements, if possible. If no valid conclusion can be drawn, write

no conclusion and explain your reasoning.

Given: An angle bisector divides an angle into two congruent angles. If two angles are congruent, then

their measures are equal.Statement: BD bisects ∠ABC.


Example 4

Draw a valid conclusion from the given statements, if possible. If no valid conclusion can be drawn, write

no conclusion and explain your reasoning.

Given: An angle bisector divides an angle into two congruent angles. If two angles are congruent, then

their measures are equal.Statement: BD bisects ∠ABC.

Conclusion: m∠ABD = m∠DBC


Problem Set


Problem Set

p. 119 #1-39 odd, 45

“Success does not consist in never making blunders, but in never making the same one a second time.”

- Josh BillingsThursday, November 6, 14

geometry section 2-4 1112

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