1. Deductive Reasoning BOMLA LacyMath Geometry Pre-AP

2. Deductive Reasoning  The use of facts, rules, definitions, or properties to reach a conclusion.

3. Deductive Reasoning  The use of facts, rules, definitions, or properties to reach a conclusion.  How is it different from Inductive?

4. Deductive Reasoning  The use of facts, rules, definitions, or properties to reach a conclusion.  How is it different from Inductive?  Inductive reasoning uses examples to make a conjecture.

5. Deductive Reasoning  Today… We’ll determine whether conclusions are valid or invalid using deductive reasoning.

6. Deductive Reasoning  Determine whether the conclusion in each example is valid based on the given information.  Example 1

7. Deductive Reasoning  Determine whether the conclusion in each example is valid based on the given information.  Example 1 The conclusion is valid using deductive reasoning.

8. Deductive Reasoning  Determine whether the conclusion in each example is valid based on the given information.  Example 2

9. Deductive Reasoning  Determine whether the conclusion in each example is valid based on the given information.  Example 2 The conclusion is invalid. The sum of the two angles is not 180.

10. Deductive Reasoning  Two Special Forms of Deductive Reasoning  Law of Detachment AND  Law of Syllogism

11. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. (If p, then q is true and p is true, then q is also true.)

12. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 1

13. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 1 What can we conclude using Law of Detachment?

14. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 1 What can we conclude using Law of Detachment? Answer: Mr. Conway is drinking coffee.

15. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 2 If the sum of two angles is 90, then the angles are complementary. The sum of two angles is 90.

16. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 2 If the sum of two angles is 90, then the angles are complementary. The sum of two angles is 90. What can we conclude using the Law of Detachment?

17. Deductive Reasoning  Law of Detachment If p  q is true and p is true, then q is also true. Example 2 If the sum of two angles is 90, then the angles are complementary. The sum of two angles is 90. What can we conclude using the Law of Detachment? Answer: The two angles are complementary.

18. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. (“If p, then q” is true and “If q, then r” is true, “If p, then r” is also true.)

19. Deductive Reasoning  Law of Syllogism Similar to the “Transitive Property of Equality”… If A = B, and B = C, then A = C.

20. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 1

21. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 1 What can we conclude using the Law of Syllogism?

22. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 1 What can we conclude using the Law of Syllogism? Answer:If I win the lottery, then I will buy a fur coat.

23. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 2 If Chuck Norris gets mad at you, then he will roundhouse kick you in the face. If Chuck Norris roundhouse kicks you in the face, then you will explode.

24. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 2 If Chuck Norris gets mad at you, then he will roundhouse kick you in the face. If Chuck Norris roundhouse kicks you in the face, then you will explode. What can we conclude using the Law of Syllogism?

25. Deductive Reasoning  Law of Syllogism If p  q is true and q  r is true, then p  r is also true. Example 2 If Chuck Norris gets mad at you, then he will roundhouse kick you in the face. If Chuck Norris roundhouse kicks you in the face, then you will explode. What can we conclude using the Law of Syllogism? Answer: If Chuck Norris gets mad at you, then you will explode.

26. Deductive Reasoning  CW – Deductive Reasoning Pg. 122, #12-17 Pg. 124, #37-42