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