2.3 Deductive Reasoning and Angle Relationships. Traditional.

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2.3 Deductive Reasoning and Angle Relationships

Traditional

Warm-Up 1) The supplement of an angle is 40 less than 8 times the measure of the angle. Find the measure of the angle and its supplement.

Deductive Reasoning The process of showing that certain statements follow logically from agreed- upon assumptions and proven facts. You are trying to prove to yourself or someone else that your conclusion is valid

1 -Make a conjecture (using what kind of reasoning?) 2 - Explain why it’s true (now what kind of reasoning?)

If an obtuse angle is bisected, then the two newly formed congruent angles are

Now let’s prove it…

Inductive vs. Deductive Reasoning Inductive Reasoning – Looking at specific examples to make a generalization. – Used to make discoveries/conjectures. Deductive Reasoning –Using generalizations to make a specific conclusion. –Used to prove conjectures.

It is possible to come to a logical conclusion that is untrue if the generalizations are not true. Ex: All teachers are bald. Mr. Scevola is a teacher. Mr. Scevola is bald.

An example of a logical deduction that is true. All angles between 90 and 180 degrees are obtuse. Angle Q is 120 degrees. Conclusion: Angle Q is obtuse.

Record the Linear Pair Conjecture in your Notes

Record the Vertical Angles Conjecture in your Notes.

Now Let’s Prove the Vertical Angles Conjecture Record this proof in your notes.

Is the converse true?

Homework Read p. 114, Do p. 117, 1, 3, 9, 26, 28, 30, 31

2.3 Deductive Reasoning and Angle Relationships

Flipped

Pop Quiz Individually, describe the differences between inductive and deductive reasoning.

Deductive Reasoning The process of showing that certain statements follow logically from agreed- upon assumptions and proven facts. You are trying to prove to yourself or someone else that your conclusion is valid

1 -Make a conjecture (using what kind of reasoning?) 2 - Explain why it’s true (now what kind of reasoning?)

If an obtuse angle is bisected, then the two newly formed congruent angles are

Now let’s prove it…

Inductive vs. Deductive Reasoning Inductive Reasoning – Looking at specific examples to make a generalization. – Used to make discoveries/conjectures. Deductive Reasoning –Using generalizations to make a specific conclusion. –Used to prove conjectures.

Record the Linear Pair Conjecture in your Notes

Record the Vertical Angles Conjecture in your Notes.

Now Let’s Prove the Vertical Angles Conjecture Record this proof in your notes.

Is the converse true?

Whiteboard Practice Problems

Warm-Up The supplement of an angle is 40 less than 8 times the measure of the angle. Find the measure of the angle and its supplement.