1. Geometry
Chapter 2
© 2004 Charlean Mullikin All rights reserved

2. Conditionals A conditional is a statement that can
be written in the If – Then form.
If the team wins the semi-final,
then they will play in the championship.

3. Conditionals The “If” part is called the Hypothesis.
If the team wins the semi-final,
then they will play in the championship.
The “Then” part is called the Conclusion.

4. Hypothesis Conclusion
Conditionals
Hypothesis Conclusion
p q
When
If Then
All
verbs
Then
Subject adjectives
are... If

5. Practice Write each statement in the if-then form:
1. The lights go out when lightning strikes the power lines.
1. If lightning strikes the power lines, then the lights will go out .
2. All squirrels are mammals.
2. If an animal is a squirrel, then it is a mammal.
3.Cheerleaders can do stunts.
3. If you are a cheerleader, then you can do stunts.
4. Complementary angles have a sum of 90.
4. If two angles are complementary angles, then they have a sum of 90.
5. The product of two odd integers is odd.
5. If two integers are odd, then their product is odd.

6. If Hypothesis Then Conclusion
Conditionals
Conditional
If Hypothesis Then Conclusion
p q
Converse
If Then
Hypothesis
Conclusion
Conclusion
Hypothesis
q p

7. Conditionals p q If the team wins the semi-final,
then they will play in the championship.
q p
Converse
If the team plays in the championship,
then they won the semi-final.
If they will play in the championship,
then the team wins the semi-final.

8. Conditionals p q q p ~ p ~ q ~ q ~ p Conditional Converse Inverse
If the team wins the semi-final,
then they will play in the championship.
p q
Converse
If the team plays in the championship,
then they won the semi-final.
q p
Inverse
If the team does not win the semi-final,
then they will not play in the championship.
~ p ~ q
Contrapositive
If the team does not play in the championship,
then they did not win the semi-final.
~ q ~ p

9. True False it could be a lion False it could be a lion True
All tigers are cats.
Conditional
If an animal is a tiger,
then it is a cat.
True
p q
False
Converse
If an animal is a cat,
then it is a tiger.
it could be a lion
q p
False
Inverse
If an animal is not a tiger,
then it is not a cat.
it could be a lion
~ p ~ q
Contrapositive
If an animal is not a cat,
then it is not a tiger.
True
~ q ~ p

10. Biconditionals True True p q q p p  q Conditional
If an angle is acute,
then it has a measure less than 90.
p q
Converse
If an angle has a measure less than 90,
then it is an acute angle.
True
q p
If both the conditional and its
Converse are true, then it can
Be written as a biconditional.
Biconditional
p  q
“if and only if”
An angle is acute if and only if
It has a measure less than 90.

11. Practice

12. Notice how the original Conditional has been
Law of Detachment
(1) p q
Notice how the original Conditional has been
Broken apart
into two pieces.
(Detached)
(2) p
(3) q

13. Law of Detachment
p q
If you pass the driving test, then you will get your license. p
Brian passed his driving test. q
Brian got his license.

14. (1) p q (2) q r (3) p r Law of Syllogism Notice how all three
statements are conditionals with three basic ideas.
The repeating part cancels out to give the conclusion.
Law of Syllogism
(1) p q
(2) q r
(3) p r

15. Law of Syllogism p q q r p r
If you pass the driving test, then you will get your license.
q r
If you get your license, then you can drive to school.
p r
If you pass the driving test, then you can drive to school.

16. If Marita gets a speeding ticket, then she will have to pay a fine.
Law of Syllogism
p q
If Marita oveys the speed limit, then she will not get a speeding ticket.
Not q r
If Marita gets a speeding ticket, then she will have to pay a fine.
No Conclusion

17. If a quadrilateral is a rectangle, then the diagonals are congruent.
Law of Syllogism
p q
If a quadrilateral is a rectangle, then the measure of each angle is 90.
q r
If the measure of each angle of a quadrilateral is 90, then the diagonals are congruent.
p r
If a quadrilateral is a rectangle, then the diagonals are congruent.

18. Law of Syllogism p q p r No Conclusion
If I lose my textbook, then I will fail my test.
p r
If I lose my textbook, then my grades will go down.
No Conclusion

19. If it is not a conditional and not a p statement, Then there is
Working the Laws
If it is not a conditional and not a p statement, Then there is
NO CONCLUSION!
Identify the p and q
If no, is it a p? Then check for Detachment.
If yes, check for syllogism.
Is 2nd statement another conditional ?

20. p q p q r q p r q Working the Laws No conclusion Law of Detachment
Law of Syllogism