2.3 Deductive Reasoningand Angle Relationships

Traditional

Warm-Up1) 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 Reasoningand 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-UpThe supplement of an angle is 40 less than 8 times the measure of the angle. Find the measure of the angle and its supplement.