Deductive Reasoning Geometry 2 3 Deductive Reasoning The

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Deductive Reasoning Geometry 2 -3

Deductive Reasoning Geometry 2 -3

• Deductive Reasoning – The process of showing that certain statements follow logically

• Deductive Reasoning – The process of showing that certain statements follow logically from agreed upon assumptions and proven facts Vocabulary

Deductive Reasoning - Example

Deductive Reasoning - Example

Deductive Reasoning - Practice

Deductive Reasoning - Practice

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

• Law of Syllogism – Combining two conditional statements when the conclusion of

• Law of Syllogism – Combining two conditional statements when the conclusion of the first statement is the hypothesis of the second statement Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning

Deductive Reasoning Konigsberg Geometry 2 -3

Deductive Reasoning Konigsberg Geometry 2 -3

• The Story The Seven Bridges of Konigsberg

• The Story The Seven Bridges of Konigsberg

The Seven Bridges of Konigsberg

The Seven Bridges of Konigsberg

• Network – A collection of points connected by paths • Traveling a

• Network – A collection of points connected by paths • Traveling a network means that the network can be drawn with a pencil without lifting the pencil off the paper, and without retracing any paths. (Points may be passed over more than once. ) Definition

• Which of the following networks can be traveled, and which are impossible

• Which of the following networks can be traveled, and which are impossible to travel? Networks

Can be traveled

Can be traveled

Can be traveled

Can be traveled

Cannot be traveled

Cannot be traveled

Can be traveled

Can be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Can be traveled

Can be traveled

Can be traveled

Can be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Cannot be traveled

Can be traveled

Can be traveled

Can be traveled

Can be traveled

Can be traveled

Can be traveled

Cannot be traveled

Cannot be traveled

Can be traveled

Can be traveled

Where would you add an eighth bridge so the network can be traveled from

Where would you add an eighth bridge so the network can be traveled from C to B?

Eighth Bridge Where would you add an eighth bridge so the network can be

Eighth Bridge Where would you add an eighth bridge so the network can be traveled from C to B?

What is the pathway?

What is the pathway?

Can you add an eighth bridge to start and end at the same point?

Can you add an eighth bridge to start and end at the same point? No, not possible

• Each intersecting point is either even or odd Conclusion

• Each intersecting point is either even or odd Conclusion

• What must happen at an odd point? You must start or end

• What must happen at an odd point? You must start or end Conclusion

• A network can be traveled if the number of odd points is

• A network can be traveled if the number of odd points is zero or two. Conjecture

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

• Pages 85 – 87 • 7, 8, 11, 14, 25, 32, 34,

• Pages 85 – 87 • 7, 8, 11, 14, 25, 32, 34, 35, 38 -41 Homework

Deductive Reasoning Deductive Reasoning Is Deductive reasoning isDeductive Reasoning Deductive Reasoning Is Deductive reasoning is
Reasoning and Proof Deductive Reasoning Deductive reasoning DeductiveReasoning and Proof Deductive Reasoning Deductive reasoning Deductive
Deductive reasoning Deductive reasoning also deductive logic orDeductive reasoning Deductive reasoning also deductive logic or
Logic Reasoning Deductive Reasoning Deductive Reasoning logically fromLogic Reasoning Deductive Reasoning Deductive Reasoning logically from
Deductive Reasoning By Mr Kass Deductive Reasoning IsDeductive Reasoning By Mr Kass Deductive Reasoning Is
Deductive Reasoning Deductive Reasoning Definition Use facts definitionsDeductive Reasoning Deductive Reasoning Definition Use facts definitions
Lesson 2 4 Deductive Reasoning Deductive reasoning usesLesson 2 4 Deductive Reasoning Deductive reasoning uses
Deductive VS Inductive Reasoning DEDUCTIVE REASONING Aristotle AncientDeductive VS Inductive Reasoning DEDUCTIVE REASONING Aristotle Ancient
Deductive Reasoning Postulates and Proofs Deductive Reasoning UsingDeductive Reasoning Postulates and Proofs Deductive Reasoning Using
Inductive vs Deductive Reasoning Deductive vs Inductive ReasoningInductive vs Deductive Reasoning Deductive vs Inductive Reasoning
Reasoning Inductive and Deductive Deductive Reasoning Process ofReasoning Inductive and Deductive Deductive Reasoning Process of
Deductive VS Inductive Reasoning DEDUCTIVE REASONING Aristotle AncientDeductive VS Inductive Reasoning DEDUCTIVE REASONING Aristotle Ancient
2 3 Apply Deductive Reasoning Use deductive reasoning2 3 Apply Deductive Reasoning Use deductive reasoning
NOTES 2 3 DEDUCTIVE REASONING DEDUCTIVE REASONING INDUCTIVENOTES 2 3 DEDUCTIVE REASONING DEDUCTIVE REASONING INDUCTIVE
Advanced Geometry Deductive Reasoning Lesson 1 Reasoning andAdvanced Geometry Deductive Reasoning Lesson 1 Reasoning and
Inductive Reasoning v Deductive Reasoning Inductive reasoning movesInductive Reasoning v Deductive Reasoning Inductive reasoning moves
REASONING Deductive reasoning syllogisms Reasoning Syllogisms are examplesREASONING Deductive reasoning syllogisms Reasoning Syllogisms are examples
Deductive Reasoning Inductive reasoning a type of reasoningDeductive Reasoning Inductive reasoning a type of reasoning
Deductive Reasoning Syllogisms Categorical syllogisms A deductive argumentDeductive Reasoning Syllogisms Categorical syllogisms A deductive argument
Deductive Reasoning BY NAME REMOVED What is DeductiveDeductive Reasoning BY NAME REMOVED What is Deductive
Deductive Reasoning What can you DD DEDUCE DeductiveDeductive Reasoning What can you DD DEDUCE Deductive
Projective Geometry Projective Geometry Projective Geometry Projective GeometryProjective Geometry Projective Geometry Projective Geometry Projective Geometry
Advanced Geometry Deductive Reasoning Lesson 2 Postulates andAdvanced Geometry Deductive Reasoning Lesson 2 Postulates and
Geometry Section 2 3 Deductive Reasoning If anGeometry Section 2 3 Deductive Reasoning If an