1. E VEN A NSWERS 2)(a)No (b)Yes (c)Yes (d)Yes (e)No (f)No 4)(a)Yes (b)Yes (c)No (d)No 6)(1)Given (2)CPCTC (3)Segment Addition Prop (4)Prop of Inequality (5)Substitution 8)(2)Segment Addition (3)Property of Inequality (4) Substitution 10)(2)Defintion ┴ lines (3)Exterior Angle Inequality Theorem (4)Substitution (5) Definition of Obtuse Angle

2. 6-2 I NVERSES AND C ONTRAPOSITIVES

3. P: HYPOTHESIS Q: CONCLUSION StatementIf p, then q ConverseIf q, then p (con-artist—does a switch) InverseIf not p, then not q Add a word In---not ContrapositiveIf not q, then not p Weirdest word—so do both, add NOT and Switch

4. EXAMPLES: Give the Inverse and Contrapos. State Tor F 1. If a parallelogram is a square, then it is a rectangle. (T) I: If a parallelogram is not a square, then it is not a rectangle (F) C+: If a parallelogram is not a rectangle, then it is not a square (T) 2. If it is snowing, then the game is canceled. I: If it is not snowing, then the game is not canceled (F) C+: If the game is not canceled, then it is not snowing (T)

5. TRY ON OWN: 1. If I can sing, then you can dance. I: If I can’t sing, then you can’t dance (F) C+: If you can’t dance, then I can’t sing (T) 2. If Taylor is not here, then he is not well. I: If Taylor is here, then he is well (F) C+: If Taylor is well, then he is here (T)

6. U SE A VENN DIAGRAM TO TELL IF AN ASSUMPTION IS T RUE OR F ALSE Example: All marathoners have stamina Statement: If you are a marathoner, then you have stamina Nick is a marathoner Heidi has stamina Mimi does not have stamina Arlo is not a marathoner Marathoner Stamina No conclusion He has stamina She is not a marathoner No conclusion

7. T RY O N O WN : A LL S QUARES A RE R HOMBUSES If it is a square, then it is a rhombus ABCD is a Rhombus PQRS is a square LAST is not a rhombus GHIJ is not a square What do we notice from this example & the last? 2 No Conclusions!! No Conclusion PQRS is a rhombus LAST is not a square No Conclusion Square Rhombus

8. RULE: The Statement and Contrapositive are logically equivalent! That means if the statement is True, the Contra+ is also True. The 2 others will be false.

9. HOMEWORK Pg 210 #1-15 all