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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 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.
