2 1 Conditional Statements by Go16d1EG

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									Conditional Statements
LESSON 2-1

             Additional Examples




                           Identify the hypothesis and the conclusion:
                If two lines are parallel, then the lines are coplanar.

         In a conditional statement, the clause after if is the hypothesis and the
         clause after then is the conclusion.


         Hypothesis: Two lines are parallel.

         Conclusion: The lines are coplanar.




                                                                             Quick Check



        HELP                                                               GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                        Write the statement as a conditional:
                An acute angle measures less than 90º.

         The subject of the sentence is “An acute angle.”

         The hypothesis is “An angle is acute.” The first part of the conditional
         is “If an angle is acute.”

         The verb and object of the sentence are “measures less than 90°.”

         The conclusion is “It measures less than 90°.” The second part of the
         conditional is “then it measures less than 90°.”

         The conditional statement is “If an angle is acute, then it measures
         less than 90°.”
                                                                             Quick Check



        HELP                                                               GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                           Find a counterexample to show that this conditional is false:
                If x2 > 0, then x > 0.

         A counterexample is a case in which the hypothesis is true and the
         conclusion is false. This counterexample must be an example in which
          x2 ≥ 0 (hypothesis true) and x ≥ 0 or x < 0 (conclusion false).
         Because any negative number has a positive square, one possible
         counterexample is x = –1.
         Because (–1)2 = 1, which is greater than 0, the hypothesis is true.
         Because –1 < 0, the conclusion is false.
         The counterexample shows that the conditional is false.

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        HELP                                                                 GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                         Use the Venn diagram below. What does it mean to be inside
                the large circle but outside the small circle?




        The large circle contains everyone who lives in California.
        The small circle contains everyone who lives in Anaheim.
        To be inside the large circle but outside the small circle means that
        you live in California but outside Anaheim.
                                                                                Quick Check



        HELP                                                              GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                           Write the converse of the conditional:
                If x = 9, then x + 3 = 12.

         The converse of a conditional exchanges the hypothesis and the conclusion.


                         Conditional                Converse

               Hypothesis      Conclusion       Hypothesis     Conclusion

                  x=9              x + 3 = 12   x + 3 = 12          x=9


         So the converse is: If x + 3 = 12, then x = 9.

                                                                             Quick Check



        HELP                                                                GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                         Write the converse of the conditional, and determine the truth
                value of each: If a2 = 25, a = 5.

         Conditional: If a2 = 25, then a = 5.

         The converse exchanges the hypothesis and conclusion.

         Converse: If a = 5, then a2 = 25.

         The conditional is false. A counterexample is a = –5: (–5)2 = 25, and –5 = 5.
                                                                                  /

         Because 52 = 25, the converse is true.



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        HELP                                                               GEOMETRY
Conditional Statements
LESSON 2-1

             Additional Examples




                         The Mad Hatter states: “You might just as well say that ‘I see
                what I eat’ is the same thing as ‘I eat what I see’!” Provide a
                counterexample to show that one of the Mad Hatter’s statements is
                false.

         The statement “I eat what I see” written as a conditional statement is
         “If I see it, then I eat it.”
         This conditional is false because there are many things you see that
         you do not eat.
         One possible counterexample is “I see a car on the road, but I do not
         eat the car.”


                                                                              Quick Check



        HELP                                                                GEOMETRY

								
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