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### 6-2 Inverses and Contrapositives

Even Answers

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

P: HYPOTHESIS Q: CONCLUSION

- Statement If p, then q
- Converse If q, then p
- (con-artist—does a switch)

- Inverse If not p, then not q
- Add a word In---not

- Contrapositive If not q, then not p
- Weirdest word—so do both, add NOT and Switch

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)

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)

Use a VENN DIAGRAM to tell if an assumption is True or False

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

Try On Own: All Squares Are Rhombuses

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

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.

HOMEWORK

- Pg 210 #1-15 all

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