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Even Answers

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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

6-2 Inverses and Contrapositives

- 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

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)

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)

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

He has stamina

No conclusion

She is not a marathoner

No conclusion

Marathoner

Stamina

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

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.

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