2.1 Conditional Statements

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# 2.1 Conditional Statements - PowerPoint PPT Presentation

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

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:
• Pp. 75-77 #4-28 all, 46-49 all.
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 x2=81, then x must equal 9.

counterexample: x could be -9

because (-9)2=81, but x≠9.

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.