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2.1 Conditional Statements. Mrs. Spitz Geometry Fall 2005. 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. Assignment:.

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2 1 conditional statements

2.1 Conditional Statements

Mrs. Spitz

Geometry

Fall 2005

standards objectives
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.
assignment
Assignment:
  • Pp. 75-77 #4-28 all, 46-49 all.
conditional statement
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 statement1
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
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
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 form1
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
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
Ex: Find a counterexample to prove the statement is false.
  • If x2=81, then x must equal 9.

counterexample: x could be -9

because (-9)2=81, but x≠9.

negation
Negation
  • Writing the opposite of a statement.
  • Ex: negate x=3

x≠3

  • Ex: negate t>5

t 5

converse
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
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
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.

slide15

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.

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