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Conditional Statements

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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.

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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…”

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Conditional Statement

• Hypothesis is the part after the word “If”• Conclusion is the part after the word “then”

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Ex: Underline the hypothesis & circle the conclusion.

• If you are a brunette, then you have brown hair.

hypothesis conclusion

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Ex: Rewrite the statement in “if-then” form

1. Vertical angles are congruent.

If there are 2 vertical angles, then they are congruent.

If 2 angles are vertical, then they are congruent.

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Ex: Rewrite the statement in “if-then” form

2. An object weighs one ton if it weighs 2000 lbs.

If an object weighs 2000 lbs, then it weighs one ton.

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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!

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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.

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Negation

• Writing the opposite of a statement.

• Ex: negate x=3

x≠3• Ex: negate t>5

t 5

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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.

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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.

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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.

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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.