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2.1 conditional statements
 

2.1 conditional statements

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    2.1 conditional statements 2.1 conditional statements Presentation Transcript

    • 2.1 Conditional Statements Mrs. Stelter Geometry Fall 2010
    • Standards/Objectives:
      • Students will learn and apply geometric concepts.
      • Objectives:
        • Recognize and analyze a conditional statement
        • Write postulates about points, lines, and planes using conditional statements.
    • Conditional Statement
      • A logical statement with 2 parts
      • 2 parts are called the hypothesis & conclusion
      • Can be written in “if-then” form; such as, “If…, then…”
    • Conditional Statement
      • Hypothesis is the part after the word “If”
      • Conclusion is the part after the word “then”
    • Ex: Underline the hypothesis & circle the conclusion.
      • If you are a brunette, then you have brown hair.
      • hypothesis conclusion
    • Ex: Rewrite the statement in “if-then” form
      • Vertical angles are congruent.
      • If there are 2 vertical angles, then they are congruent.
      • If 2 angles are vertical, then they are congruent.
    • Ex: Rewrite the statement in “if-then” form
      • An object weighs one ton if it weighs 2000 lbs.
      • If an object weighs 2000 lbs, then it weighs one ton.
    • Counterexample
      • Used to show a conditional statement is false.
      • It must keep the hypothesis true, but the conclusion false!
      • It must keep the hypothesis true, but the conclusion false!
      • It must keep the hypothesis true, but the conclusion false!
    • Ex: Find a counterexample to prove the statement is false.
      • If x 2 =81, then x must equal 9.
      • counterexample: x could be -9
      • because (-9) 2 =81, but x ≠9.
    • Venn Diagrams Dogs labs If it is a lab, then it is a dog Michigan Detroit If you live in Detroit, then you live in Michigan
    • Negation
      • Writing the opposite of a statement.
      • Ex : negate x=3
      • x ≠3
      • Ex : negate t>5
      • t 5
    • Converse
      • Switch the hypothesis & conclusion parts of a conditional statement.
      • Ex: Write the converse of “If you are a brunette, then you have brown hair.”
      • If you have brown hair, then you are a brunette.
    • Inverse
      • Negate the hypothesis & conclusion of a conditional statement.
      • Ex : Write the inverse of “If you are a brunette, then you have brown hair.”
      • If you are not a brunette, then you do not have brown hair.
    • Contrapositive
      • Negate, then switch the hypothesis & conclusion of a conditional statement.
      • Ex : Write the contrapositive of “If you are a brunette, then you have brown hair.”
      • If you do not have brown hair, then you are not a brunette.
    • The original conditional statement & its contrapositive will always have the same meaning. The converse & inverse of a conditional statement will always have the same meaning.
    • Assignment:
      • Pp. 83 (2-34)
      • Pp. 85 (54-58)