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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.


2 1 conditional statements

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.