Conditional Statements. Standards/Objectives: Students will learn and apply geometric concepts. Objectives: –Recognize and analyze a conditional statement.

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Presentation transcript:

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 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. hypothesisconclusion

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.

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.

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!

Ex: Find a counterexample to prove the statement is false. If x 2 =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.