A statement in the form “If _, then .” is called a __. A conditional statement has two parts: Ex1)

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A statement in the form “If _____, then ______.” is called a ______________________ ______________________. A conditional statement has two parts: Ex1) If today is Monday, then yesterday was Sunday. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Ex2) If x = 5, then 2x = 10. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Ex3) If x = 6, then x 2 = 36. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Sometimes you may see conditional statements in other forms. When this happens, it is helpful to rewrite the statement in the “if…then…” format. Ex4) 3x + 2 = -13 implies that x = -5. Rewrite as _____________________________________________________________ Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Ex5) A number is divisible by 2 if it is divisible by 6. Rewrite as _____________________________________________________________ Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Section 2.1, 3.6 Notes Conditional Statements, Inductive & Deductive Reasoning

To find the _______________ of a conditional statement, you must switch the hypothesis and conclusion. Ex6) If today is Monday, then yesterday was Sunday. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Not all converses will be true. Ex7) If you live in Doylestown, then you live in Pennsylvania. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is this converse true? ______. In order to prove that a converse is false, you must provide a ____________________. A ____________________________________________________________________ ______________________________________________________________________ Counterexample for Ex7: __________________________________________________ Example: For the conditional statement, (a) identify the hypothesis and conclusion, (b) write the converse of the statement and determine if the converse is true or false. (c) If the converse is false, provide a counterexample. Ex8) __________________________________________________________________ (a) Hypothesis: ________________________________________________________ Conclusion: _________________________________________________________ (b) Converse: __________________________________________________________ Is the converse true or false? _____________ (c) If false, write a counterexample: _________________________________________ Section 2.1, 3.6 Notes Conditional Statements, Inductive & Deductive Reasoning

________________________ use the phrase “if and only if” to indicate when a conditional and its converse are both true. Rewrite the conditional from the first example as a biconditional: ____________________________________________________________________. You can rewrite any ______________________ as a biconditional. Ex1: __________________________________________________________________ ______________________________________________________________________ Rewrite: _______________________________________________________________ ______________________________________________________________________ Ex2: __________________________________________________________________ ______________________________________________________________________ Rewrite: _______________________________________________________________ ______________________________________________________________________ Section 2.1, 3.6 Notes Conditional Statements, Inductive & Deductive Reasoning Section 3.6 Inductive vs. Deductive Reasoning Deductive Reasoning Definition: Drawing conclusions based on ______________________________________ _____________________________________________________________________. Deductive Reasoning takes _________________________________________________ _____________________________________________________________________. ______________________ to _____________________ Inductive Reasoning Definition: Drawing conclusions based on _____________________________________ _____________________________________________________________________. Inductive Reasoning takes __________________________________________________ ______________________________________________________________________ _____________________________________________________________________ _____________________ to ______________________ KEY WORD: _____________________

Examples: Determine whether each scenario’s conclusion is reached based on inductive or deductive reasoning. 1. In biology class you learned that one characteristic of mammals is that they are all warm- blooded. You conclude that your dog must be warm-blooded. 2. Every type of fish that you have seen at the aquarium has been a vertebrate. You conclude that all fish are vertebrates. 3. After studying the biographies of the past 30 Pennsylvania Senators, you observe that each Senator has been older than 36. You conclude that one requirement for being a senator is that you must be older than In American Political Systems you learned that one requirement to be President of the United States is that you must be a natural born citizen. You conclude that Bill Clinton is a natural born citizen. Section 2.1, 3.6 Notes Conditional Statements, Inductive & Deductive Reasoning

Geometry/Trig 2Name: __________________________ 2-1 Check for UnderstandingDate: ___________________________ Directions: For each conditional statement, identify the hypothesis and conclusion, write the converse of the statement and determine if the converse is true or false. If the converse is false, provide a counterexample. #1. If x = -2, then x 2 = 4. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is the converse true or false? ______________________________________________ If false, write a counterexample: ____________________________________________ #2. If m  ABC = 40, then  ABC is not obtuse. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is the converse true or false? ______________________________________________ If false, write a counterexample: ____________________________________________ #3. AB = CD implies AB  CD. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is the converse true or false? ______________________________________________ If false, write a counterexample: ____________________________________________ #4. If b > 4, then 5b > 20. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is the converse true or false? ______________________________________________ If false, write a counterexample: ____________________________________________ #5. If I live in Warrington, then I live in Pennsylvania. Hypothesis: ____________________________________________________________ Conclusion: _____________________________________________________________ Converse: ______________________________________________________________ Is the converse true or false? ______________________________________________ If false, write a counterexample: ____________________________________________

Geometry/Trig 2Name: _________________________ 3-6 Check for UnderstandingDate: __________________________ Directions: Determine whether each scenario’s conclusion is reached based on inductive or deductive reasoning. 1. Jared noticed that spaghetti had been served in the cafeteria for the last 5 Wednesdays in a row. Jared concludes that the school always serves spaghetti on Wednesdays. 2. Carrie has gotten a sunburn every time that she has gone to the beach. She concludes that she will get sunburn when she goes this Saturday. 3. Kelly learned in geometry class that a triangle with three congruent sides is called an equilateral triangle. Kelly concludes that the triangle that she drew with side lengths 5 inches, 5 inches, and 5 inches is an equilateral triangle. 4. You are looking at a diagram of segment AB and point C on segment AB. The given information states that C is the midpoint of AB. You conclude that AC  CB. 5. Rachel reads the school cafeteria menu information that was sent home. She reads that every Thursday the cafeteria will serve turkey sandwiches. Rachel concludes that today, Thursday, September 20, the cafeteria will be serving turkey sandwiches. 6. Becky has observed that every school day at 1:00pm there are afternoon announcements. Becky concludes that there will be afternoon announcements today at 1:00pm. 7. Greg has observed that all reptiles that he has studies have been green. Greg concludes that all reptiles are green. 8. Keith learned in American Political Systems that to be eligible to be elected into the House of Representatives, you must be at least 25 years old. He concludes that our Representative, Patrick Murphy, is at least 25 years old. 9. Every poem that Monica has read rhymes. Monica concludes that all poems rhyme. 10. Eric learned in English class that Sonnets (a type of poem) follow a specific rhyme scheme. Eric concludes that Shakespeare’s Sonnet XII will follow that rhyme scheme.