1. Overview of Sections 1.1, 2.1-2.3 Sections 1.1, 2.1, 2,2 and 2.3 Combined like Transformers!

2. 1.1 Patterns and Inductive Reasoning SWBAT: To Use Inductive Reasoning to make conjectures.

3. What is Inductive Reasoning? Inductive Reasoning is reasoning based on patterns you observe.

4. Conjecture A conclusion that is reached using inductive reasoning is a Conjecture Not all conjectures are true and can be proved false with just one counterexample

5. 2.1 Conditional Statements SWBAT: To Recognize Conditional Statements To Write Converses of Conditional Statements

6. Conditional Statements A Conditional Statement is an if-then statement. If you behave, then we’ll get Ice Cream If you do your homework, then you will pass! If it rains outside, then you need an umbrella. The part following “If” is the Hypothesis. The part following “Then” is the Conclusion

7. Identify Hypothesis and Conclusion If it is the first day of fall, then the month is September. Hypothesis : It is the First Day of Fall Conclusion: The month is September.

8. Identify Hypothesis and Conclusion If x + 2 = 5, then x = 3. Hypothesis : x + 2 = 5 Conclusion: x = 3

9. Writing a Conditional Be careful when writing a conditional, the order you say it must make sense! A rectangle has four sides. If a figure is a Rectangle then it has four sides. (Sounds good…) If a figure has four sides, then it is a Rectangle? (Doesn’t make sense, trapezoid, parallelogram…)

10. Truth Value A Conditional Statement is considered true if both hypothesis and conclusion are both true. A Counterexample is one case where the hypothesis is true but a different conclusion happens… You only need one counterexample to prove a Conditional statement false.

11. Finding A Counterexample If it is February, then there are only 28 days in the month. Counterexample: Leap Year. In a leap year February has 29 days…

12. Converse The Converse of a Conditional Flips the Hypothesis and Conclusion

15. Biconditionals & Definitions A biconditional is a statement that combines both a conditional and its converse when they are both true Uses the phrase “if and only if” It is a good definition

16. Deductive Reasoning  The process of reasoning logically from given statements to a conclusion **if the statements are true, a true conclusion would be produced

17. Using deductive reasoning If it is Monday and the Giants won Sunday, then Mr. Falcicchio is happy.  Today is Monday and the Giants won Sunday. What can you conclude?  Today is Monday and Mr. Falcicchio is happy. What can you conclude?

18. Using deductive reasoning If two lines are perpendicular, then they intersect to form right angles.  Line AC is perpendicular to Line BD. What can you conclude?

19. Using deductive reasoning If there is a Will Ferrell movie, then Mr. Carucci will watch it. If Mr. Carucci watches it, then he will say 90 Will Ferrell quotes and annoy Ms. Okul.  Ms. Okul is annoyed. What can you conclude?  Will Ferrell will be in Anchorman 2 in December. What can you conclude?

20. Using deductive reasoning If two angles are supplementary and congruent, then they are right angles. If an angle is right angles, then its measure 90 degrees.  <1 and <2 are supplementary and congruent. What can you conclude?  m<3=90. What can you conclude?