2.3 deductive reasoning and angle relationships. traditional
TRANSCRIPT
![Page 1: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/1.jpg)
2.3 Deductive Reasoningand Angle Relationships
![Page 2: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/2.jpg)
Traditional
![Page 3: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/3.jpg)
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.
![Page 4: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/4.jpg)
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
![Page 5: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/5.jpg)
1 - Make a conjecture (using what kind of reasoning?)
2 - Explain why it’s true(now what kind of reasoning?)
![Page 6: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/6.jpg)
If an obtuse angle is bisected, then the two newly formed congruent angles are
![Page 7: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/7.jpg)
Now let’s prove it…
![Page 8: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/8.jpg)
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.
![Page 9: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/9.jpg)
• 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.
![Page 10: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/10.jpg)
• 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.
![Page 11: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/11.jpg)
Record the Linear Pair Conjecture in your Notes
![Page 12: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/12.jpg)
Record the Vertical Angles Conjecture in your Notes.
![Page 13: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/13.jpg)
Now Let’s Prove the Vertical Angles Conjecture
• Record this proof in your notes.
![Page 14: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/14.jpg)
Is the converse true?
![Page 15: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/15.jpg)
![Page 16: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/16.jpg)
![Page 17: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/17.jpg)
Homework
• Read p. 114, Do p. 117, 1, 3, 9, 26, 28, 30, 31
![Page 18: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/18.jpg)
2.3 Deductive Reasoningand Angle Relationships
![Page 19: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/19.jpg)
Flipped
![Page 20: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/20.jpg)
Pop Quiz
• Individually, describe the differences between inductive and deductive reasoning.
![Page 21: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/21.jpg)
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
![Page 22: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/22.jpg)
1 - Make a conjecture (using what kind of reasoning?)
2 - Explain why it’s true(now what kind of reasoning?)
![Page 23: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/23.jpg)
If an obtuse angle is bisected, then the two newly formed congruent angles are
![Page 24: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/24.jpg)
Now let’s prove it…
![Page 25: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/25.jpg)
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.
![Page 26: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/26.jpg)
Record the Linear Pair Conjecture in your Notes
![Page 27: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/27.jpg)
Record the Vertical Angles Conjecture in your Notes.
![Page 28: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/28.jpg)
Now Let’s Prove the Vertical Angles Conjecture
• Record this proof in your notes.
![Page 29: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/29.jpg)
Is the converse true?
![Page 30: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/30.jpg)
![Page 31: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/31.jpg)
• Whiteboard Practice Problems
![Page 32: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/32.jpg)
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.
![Page 33: 2.3 Deductive Reasoning and Angle Relationships. Traditional](https://reader035.vdocuments.site/reader035/viewer/2022081603/56649ddb5503460f94ad2c08/html5/thumbnails/33.jpg)