Chapter 6: Inequalities in Geometry

1. Chapter 6: Inequalities in Geometry • 6.2 – Inverses and Contrapositives • 6.3 – Indirect Proof (proof by contradiction) • 6.4 – Triangle Inequalities

2. TRUE False 6.2 – Inverses and Contrapositives TRUE False 12/10 Conditional: If p, then q. Converse: If q, then p. Inverse: If not p, then not q. Contrapositive: If not q, then not p. Venn Diagram representation: Conditional: Contrapositive: A conditional statement and its contrapositiveare logically equivalent. (True-True or False-False) p q

3. TRUE False TRUE False 6.2 – Inverses and Contrapositives q p Conditional: If p, then q. Converse: If q, then p. Inverse: If not p, then not q. Contrapositive: If not q, then not p. Venn Diagram representation: Converse: Inverse: A conditional statement is not logically equivalent to its converse or its inverse. But, the converse and the inverseare logically equivalent statements. (True-True or False-False)

4. If you live in Castro Valley, then you live in CA. TRUE If you live in CA, then you live in Castro Valley. 6.2 – Inverses and Contrapositives False If you don’t live in Castro Valley, then you don’t live in CA. False Example 1: Conditional: Converse: Inverse: Contrapositive: If you don’t live in CA, then you don’t live in Castro Valley. TRUE Oakland San Francisco Los Angeles Hayward Castro Valley CA

5. If you are a runner, then you are an athlete. TRUE If you are an athlete, then you are a runner. 6.2 – Inverses and Contrapositives False If you are not a runner, then you are not an athlete. False Example 2: Conditional: Converse: Inverse: Contrapositive: If you are not an athlete, then you are not a runner. TRUE Cyclist Basketball player Football player Skier Athlete Runner

6. If x2 = 16. then x = 4. False 6.2 – Inverses and Contrapositives If x = 4, then x2 = 16. TRUE If x2≠ 16, then x ≠ 4. TRUE Example 3: Conditional: Converse: Inverse: Contrapositive: If x ≠ 4, then x2 ≠ 16. False TRICKY: x = -4 x = 4 x2 = 16

7. If a quadrilateral is regular, then it is a square. TRUE If a quadrilateral is a square, then it is regular. 6.2 – Inverses and Contrapositives TRUE If a quadrilateral is not regular, then it is not a square. TRUE Example 4: Conditional: Converse: Inverse: Contrapositive: If a quadrilateral is not a square, then it is not regular. TRUE TRICKY: Not Regular Not Square Regular Square

8. Math teachers assign hours of homework. (True Conditional) Assign hours of HW Math Teacher 6.2 – Inverses and Contrapositives If you are a math teacher, then you assign hours of HW. Bridget Sullivan assigns hours of HW. Example 5: (Page 211 W.E. #12) Given: A) Bridget Sullivan is a math teacher. B) August Campos assigns hours of homework. C) Andrew Byrnes assigns no homework at all. D) Jason Babler is not a math teacher. NEI (Not Enough Information) Andrew Byrnes is not a math teacher. No conclusion

9. Classroom Practice Scavenger Hunt!