1. Warm-up: What is the next term in the sequence? 1)3, 5, 11, 21, 35, ___ 2)

2. Objective: Students will write the inverse, converse, and contrapositive of a conditional statement. HW: - pg 75 #1-37 eoo

3. Review Homework Answers to even problems Pg 898: 2: 0.03125 4: 9.0 6: 42 8: X=0

4. Inductive Reasoning Inductive Reasoning: a type of reasoning in which the conclusion is based on several past observations Ex: –2, 5, 8, 11, 14, ___, ___ –We have had pop quizzes on Friday for the past four weeks… Using inductive reasoning you would conclude that we would likely have a quiz every Friday.

5. Deductive Reasoning Deductive Reasoning: a type of reasoning in which the conclusion is based on accepted statements. We used deductive reasoning to come up with the formula for the Distance Formula. Pythagorean Theorem

6. Conditional Statement (“If-then” statements) If it’s raining, then the game is canceled. –If p, then q. Hypothesis = it’s raining (“the condition”) Conclusion = the game is canceled.

7. Notation If it’s raining, then the game is canceled. Hypothesis = p = it’s raining Conclusion= q = the game canceled ~p = (“not p”) it is NOT raining. ~q = (“not q”) the game is NOT canceled. = implies

8. The Converse of a Conditional Statement If it’s raining, then the game is canceled. –If p, then q. If the game is canceled, then it’s raining. –If q, then p. The hypothesis and the conclusion are interchanged.

9. The Inverse of a Conditional Statement If it’s raining, then the game is canceled. –If p, then q. If it’s NOT raining, then the game is NOT canceled. –If not p, then not q. The hypothesis and the conclusion are negated.

10. The Contrapositive of a Conditional Statement If it’s raining, then the game is canceled. –If p, then q. If the game is NOT canceled, then it’s NOT raining. –If not q, then not p. The hypothesis and the conclusion are interchanged and negated.

11. Summary Original Converse Inverse Contrapositive

12. Example If you mow the lawn, then I will give you $10. What is the hypothesis? What is the conclusion? Write the converse of this statement. Write the inverse of this statement. Write the contrapositive of this statement.

13. Example If two angles are a linear pair, then the two angles are supplementary. (T/F) What is the hypothesis? What is the conclusion?

14. Example: Converse If two angles are a linear pair, then the two angles are supplementary. (T/F) Converse: If the two angles are supplementary, then the two angles are a linear pair. (T/F) 120° 60° 120°

15. Example: Inverse If two angles are a linear pair, then the two angles are supplementary. (T/F) Inverse: If two angles are not a linear pair, then the two angles are not supplementary. (T/F) 120° 60° 120°

16. Example: Contrapositive If two angles are a linear pair, then the two angles are supplementary. (T/F) Contrapositive: If two angles are not supplementary, then the two angles are not a linear pair. (T/F) 120° 60° 120°