1. 2.4 Deductive Reasoning
2.4 Deductive Reasoning

2. Objectives: Use the Law of Detachment and Law of Syllogism.
2.4 Deductive Reasoning

3. Vocabulary: Deductive Reasoning Inductive Reasoning Law of Detachment
Law of Syllogism
2.4 Deductive Reasoning

4. SOLVE IT!
2.4 Deductive Reasoning

5. Deductive vs. Inductive Reasoning
The difference:
inductive reasoning uses patterns to arrive at a conclusion (conjecture)
deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion.
2.4 Deductive Reasoning

6. Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

7. Examples of Inductive Reasoning
Every quiz has been easy. Therefore, the test will be easy.
The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow.
Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.
2.4 Deductive Reasoning

8. Example of Deductive Reasoning
The catalog states that all entering freshmen must take a mathematics placement test.
An Example:
You are an entering freshman.
Conclusion: You will have to take a mathematics placement test.
2.4 Deductive Reasoning

9. Inductive or Deductive Reasoning?
Geometry example…
60◦ x
Triangle sum property –
the sum of the angles of any triangle is always 180 degrees.
Therefore, angle x = 30°
Deductive Reasoning – conclusion is based on a property
2.4 Deductive Reasoning

10. Inductive or Deductive Reasoning?
Geometry example…
What comes next?
Is there a rule?
Colored triangle rotating 90° CW in the corners of the square
Inductive Reasoning
2.4 Deductive Reasoning

11. 2.4 Deductive Reasoning

12. 2.4 Deductive Reasoning

13. Deductive Reasoning Is…
Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true.
For Example
All dogs have a tail.
Buddy is a dog.
Therefore Buddy has a tail.
2.4 Deductive Reasoning

14. How Can Deductive Reasoning Be Applied In School?
Math
Scott has a case of soda in his house since there are 13 cans of soda left I deduce that Scott has drank 11 cans of soda.
English
When I see ‘like’ in a sentence, I deduce that it is a simile.
2.4 Deductive Reasoning

15. Using laws and rules to make assumptions
Science
Using laws and rules to make assumptions
The law of gravity means everything that goes up must come down I threw a baseball in the air That means the baseball must come down.
Social Studies
To be elected President you must obtain at least 270 electoral votes George Bush won 287 electoral votes Therefore George Bush is the President.
2.4 Deductive Reasoning

16. 2.4 Deductive Reasoning

17. Law of Detachment:
You can use this law to provide conclusions to statements.
2.4 Deductive Reasoning

18. If M is the midpoint of a segment, then it divides the segment into two congruent segments. Given: M is the midpoint of .
You can conclude that M divides into two congruent segments, or
2.4 Deductive Reasoning

19. If an angle is obtuse, then it is not acute. is not obtuse.
The converse of the assumption is not true, so It is not possible to conclude that is acute.
2.4 Deductive Reasoning

20. Law of Syllogism:
You can use this law to state a conclusion from two true conditional statement.
2.4 Deductive Reasoning

21. If you practice your math, then you will get good grades.
If a figures is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion: if the figure is a square, then the figure has four side.
If you practice your math, then you will get good grades.
If you get good grades in math, then you will pass the class.
Conclusion: if you practice your math, then you will pass the class.
2.4 Deductive Reasoning

22. Lesson Check:
2.4 Deductive Reasoning

23. Lesson Check:
2.4 Deductive Reasoning