2.3 Deductive Reasoning and Angle Relationships. Traditional.
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Transcript of 2.3 Deductive Reasoning and Angle Relationships. Traditional.
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.