Chapter 1 - Warm-ups 09/03 page 7 #1-10 all (WE) 09/08 page 14 #1-20 all (CE) 09/12 page 20 #2-26 even (CE) 09/16 Self-Test 2 page 29 #1-12 all.

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Presentation transcript:

Chapter 1 - Warm-ups 09/03 page 7 #1-10 all (WE) 09/08 page 14 #1-20 all (CE) 09/12 page 20 #2-26 even (CE) 09/16 Self-Test 2 page 29 #1-12 all

Chapter 2: Deductive Reasoning

Conditional Statement: If hypothesis, then conclusion. hypothesis - _____________________________ conclusion - _____________________________ converse – conditional statement in which the ______________ and the _______________ are switched. If ______________, then _______________. counterexample – an example that refutes or disproves a hypothesis, proposition, or theorem. after “if” p after “then” q hypothesis Ifconclusion then hypothesis q conclusion p

Conditional statements are not always written with the “if” clause first. Here are some examples. All these conditionals mean the same thing. General form:Examples: If p, then q.If x 2 = 25, then x < 10. p implies q.x 2 = 25, implies x < 10. p only if q.x 2 = 25 only if x < 10. q if p. x < 10 if x 2 = 25.

4. I’ll dive if you dive. 5. If a = b, then a + c = b + c.

If the conditional or converse is false, provide a counterexample. 6. If today is Thursday, then tomorrow is Friday. Hypothesis: ____________________________ Conclusion: ____________________________ Converse: _____________________________ _____________________________ Conditional: True or False Converse: True or False today is Thursday tomorrow is Friday It tomorrow is Friday, then today is Thursday.

7. If you have a 95, then you have an A. Hypothesis: _________________________ Conclusion: _________________________ Converse: __________________________ __________________________ Conditional: True or False Converse: True or False you have a 95 you have an A. If you have an A, then you have a 95.

8. If Lisa lives in Langhorne, then she lives in PA. Hypothesis: _____________________________ Conclusion: _____________________________ Converse: _____________________________ _____________________________ Conditional: True or False Converse: True or False Lisa lives in Langhorne she lives in PA If Lisa lives in PA, then she lives in Langhorne.

9. If x = 5, then 4x = 20. Hypothesis: _____________________________ Conclusion: _____________________________ Converse: _____________________________ Conditional: True or False Converse: True or False x = 5 4x = 20 If 4x = 20, then x = 5.

10. If x = 2, then x 2 = 4. Hypothesis: ____________________________ Conclusion: ____________________________ Converse: ____________________________ Conditional: True or False Converse: True or False x = 2 x 2 = 4 If x 2 = 4, then x = 2.

Bi – Conditional: “if and only if” or iff ________________ if and only if _________________. Ex.Congruent angles are angles that have congruent measures. ___________________________________________ Ex. Obtuse angles are angles with measures between 90  and 180 . ___________________________________________ hypothesis pconclusion q Angles are congruent angles if and only if they have congruent measures. Angles are obtuse angles if and only if their measures are between 90⁰ and 180⁰.

HOMEWORK Page 35 #2-30 even