2.1 Conditional Statements

1. 2.1 Conditional Statements Mr. Robinson Geometry Fall 2011

2. Essential Question: • How do you recognize and use conditional statements? • What are other important postulates?

3. 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…”

4. Conditional Statement • The Hypothesis is part of the conditional that COULD happen. It usually follows after the IF. • The Conclusion is the part of the conditional that results from the hypothesis. It follows after the THEN.

5. Ex: Underline the hypothesis & circle the conclusion. • If it snows, then school is canceled. hypothesis conclusion

6. 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.

7. 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.

8. When is a Conditional True??? Your mom promises: “If you make an A in Geometry, she will give you $100.” You make an A, she pays $100. You make an A, she doesn’t pay $100. You don’t make an A, she pays $100. You don’t make an A, she doesn’t pay $100.

9. When is a Conditional True???

10. 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!

11. 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.

12. Negation • Writing the opposite of a statement. • Ex: negate x=3 x≠3 • Ex: negate t>5 t 5

13. Ex: Venn Diagrams for hypothesis & conclusion. School is Canceled Snow “If it snows, then school is canceled.”

14. Converse • Switch the hypothesis & conclusion parts of a conditional statement. • Ex: Write the converse of “If it snows, then school is canceled.” If school is canceled, then it has snowed.

15. Inverse • Negate the hypothesis & conclusion of a conditional statement. • Ex: Write the inverse of “If it snows, then school is canceled.” If it has not snowed, then school has not been canceled.

16. Contrapositive • Negate, then switch the hypothesis & conclusion of a conditional statement. • Ex: Write the contrapositive of “If it snows, then school is canceled.” If school has not been canceled, then it has not snowed.

17. Conditional Equivalence • The original conditional statement & its contrapositive will always have the same meaning: • Original: If it snows, then school is canceled. • Contrapositive: If school has not been canceled, then it has not snowed.

18. Conditional Equivalence The converse & inverse of a conditional statement will always have the same meaning. Converse: If school is canceled, then it has snowed. Inverse: If it has not snowed, then school has not been canceled.

19. Other Postulates • Postulate 5: Through any two points there exists exactly one line. • Postulate 6: A line contains at least 2 points. • Postulate 7: If 2 lines intersect, then their intersection is exactly 1 point.

20. Other Postulates • Postulate 8: through any three noncollinear points there exists exactly 1 plane. • Postulate 9: A plane contains at least three noncollinear points. • Postulate 10: If any two points lie in a plane, then the line containing them lies in the plane.

21. Other Postulates • Postulate 11: If 2 planes intersect, then their intersection is a line.

22. Assignment: • P 75: 10 – 48 even