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# 2.1 conditional statements

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### 2.1 conditional statements

1. 1. 2.1 Conditional Statements Mrs. Stelter Geometry Fall 2010
2. 2. Standards/Objectives: <ul><li>Students will learn and apply geometric concepts. </li></ul><ul><li>Objectives: </li></ul><ul><ul><li>Recognize and analyze a conditional statement </li></ul></ul><ul><ul><li>Write postulates about points, lines, and planes using conditional statements. </li></ul></ul>
3. 3. Conditional Statement <ul><li>A logical statement with 2 parts </li></ul><ul><li>2 parts are called the hypothesis & conclusion </li></ul><ul><li>Can be written in “if-then” form; such as, “If…, then…” </li></ul>
4. 4. Conditional Statement <ul><li>Hypothesis is the part after the word “If” </li></ul><ul><li>Conclusion is the part after the word “then” </li></ul>
5. 5. Ex: Underline the hypothesis & circle the conclusion. <ul><li>If you are a brunette, then you have brown hair. </li></ul><ul><li> hypothesis conclusion </li></ul>
6. 6. Ex: Rewrite the statement in “if-then” form <ul><li>Vertical angles are congruent. </li></ul><ul><li>If there are 2 vertical angles, then they are congruent. </li></ul><ul><li>If 2 angles are vertical, then they are congruent. </li></ul>
7. 7. Ex: Rewrite the statement in “if-then” form <ul><li>An object weighs one ton if it weighs 2000 lbs. </li></ul><ul><li>If an object weighs 2000 lbs, then it weighs one ton. </li></ul>
8. 8. Counterexample <ul><li>Used to show a conditional statement is false. </li></ul><ul><li>It must keep the hypothesis true, but the conclusion false! </li></ul><ul><li>It must keep the hypothesis true, but the conclusion false! </li></ul><ul><li>It must keep the hypothesis true, but the conclusion false! </li></ul>
9. 9. Ex: Find a counterexample to prove the statement is false. <ul><li>If x 2 =81, then x must equal 9. </li></ul><ul><li>counterexample: x could be -9 </li></ul><ul><li>because (-9) 2 =81, but x ≠9. </li></ul>
10. 10. Venn Diagrams Dogs labs If it is a lab, then it is a dog Michigan Detroit If you live in Detroit, then you live in Michigan
11. 11. Negation <ul><li>Writing the opposite of a statement. </li></ul><ul><li>Ex : negate x=3 </li></ul><ul><li>x ≠3 </li></ul><ul><li>Ex : negate t>5 </li></ul><ul><li>t 5 </li></ul>
12. 12. Converse <ul><li>Switch the hypothesis & conclusion parts of a conditional statement. </li></ul><ul><li>Ex: Write the converse of “If you are a brunette, then you have brown hair.” </li></ul><ul><li>If you have brown hair, then you are a brunette. </li></ul>
13. 13. Inverse <ul><li>Negate the hypothesis & conclusion of a conditional statement. </li></ul><ul><li>Ex : Write the inverse of “If you are a brunette, then you have brown hair.” </li></ul><ul><li>If you are not a brunette, then you do not have brown hair. </li></ul>
14. 14. Contrapositive <ul><li>Negate, then switch the hypothesis & conclusion of a conditional statement. </li></ul><ul><li>Ex : Write the contrapositive of “If you are a brunette, then you have brown hair.” </li></ul><ul><li>If you do not have brown hair, then you are not a brunette. </li></ul>
15. 15. 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.
16. 16. Assignment: <ul><li>Pp. 83 (2-34) </li></ul><ul><li>Pp. 85 (54-58) </li></ul>