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# Conditional Statements - PowerPoint PPT Presentation

Conditional Statements. 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

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## PowerPoint Slideshow about 'Conditional Statements' - breck

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### Conditional Statements

• Students will learn and apply geometric concepts.

• Objectives:

• Recognize and analyze a conditional statement

• Write postulates about points, lines, and planes using conditional statements.

• A logical statement with 2 parts

• 2 parts are called the hypothesis & conclusion

• Can be written in “if-then” form; such as, “If…, then…”

• Hypothesis is the part after the word “If”

• Conclusion is the part after the word “then”

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

hypothesis conclusion

• Vertical angles are congruent.

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

If 2 angles are vertical, then they are congruent.

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

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

• 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!

• If x2=81, then x must equal 9.

counterexample: x could be -9

because (-9)2=81, but x≠9.

• Writing the opposite of a statement.

• Ex: negate x=3

x≠3

• Ex: negate t>5

t 5

• 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.

• 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.

• 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.