1. Geometry Drill 10/7/13
Aki, Bard, and Coretta live in
Albany, Biloxi, and Chicago.
No one lives in a city that begins
with the same letter as her name.
Aki writes letters to her friend in
Chicago. Who lives in what
city? #??

2. Identify, write, and analyze the
truth value of conditional
statements.
Write the inverse, converse,
and contrapositive of a
conditional statement.
Objectives

3. conditional statement
hypothesis
conclusion
truth value
negation
converse
inverse
contrapostive
logically equivalent statements
Vocabulary

4. By phrasing a conjecture as an if-
then statement, you can quickly
identify its hypothesis and
conclusion.

5. Vocabulary
Conditional statement
A statement written in the
form IF___,THEN___.
If P, then Q.
P –> Q (NOTATION)

6. Vocabulary
Conditional statements:
If P, then Q
P implies Q
Q, if P
ALL MEAN SAME THING

7. Vocabulary
Hypothesis-statement
following the word
“if”.
Conclusion-statement
following the word
“then”.

8. FACT OR FICTION???
IF TWO ANGLES ARE
SUPPLEMENTARY, T
HEN THEY ARE BOTH
RIGHT ANGLES.

9. REVERSE THE
HYPOTHESIS &
CONCLUSION

10. FACT OR
FICTION???
IF TWO ANGLES ARE
RIGHT ANGLES, THEN
THEY ARE
SUPPLEMENTARY
ANGLES.

11. VOCABULARY
CONVERSE- A
conditional statement
with the hypothesis and
conclusion
interchanged.
If Q, then P. Q –>P

12. FACT OR
FICTION???
If x = 4, then x2 = 16

13. Is the converse true?
If x2 = 16, then x = 4.

14. Write the converse. Is the
converse true?
1. If two angles are
vertical , then they are
congruent.
2. If x > 0, then x2 > 0.

15. The negation of
statement p is “not p,”
written as ~p. The
negation of a true
statement is false, and
the negation of a false
statement is true.

16. Definition
Symbol
s
The converse is
the statement
formed by
exchanging the
hypothesis and
conclusion.
q  p

17. Definition
Symbol
s
The inverse is
the statement
formed by
negating the
hypothesis and
conclusion.
~p  ~q

18. Definition Symbols
The contrapositive
is the statement
formed by both
exchanging and
negating the
hypothesis and
conclusion.
~q  ~p

19. Write the converse, inverse, and contrapositive
of the conditional statement. Use the Science
Fact to find the truth value of each.
Example 4: Biology Application
If an animal is an adult insect, then it has six
legs.

20. Example 4: Biology Application
Inverse: If an animal is not an adult insect, then it does
not have six legs.
Converse: If an animal has six legs, then it is an adult
insect.
If an animal is an adult insect, then it has six legs.
No other animals have six legs so the converse is true.
Contrapositive: If an animal does not have six legs,
then it is not an adult insect.
Adult insects must have six legs. So the contrapositive
is true.
No other animals have six legs so the converse is true.

21. Write the converse, inverse, and contrapostive
of the conditional statement “If an animal is a
cat, then it has four paws.” Find the truth value
of each.
Check It Out! Example 4
If an animal is a cat, then it has four paws.

22. Check It Out! Example 4
Inverse: If an animal is not a cat, then it does not
have 4 paws.
Converse: If an animal has 4 paws, then it is a cat.
Contrapositive: If an animal does not have 4 paws,
then it is not a cat; True.
If an animal is a cat, then it has four paws.
There are other animals that have 4 paws that are not
cats, so the converse is false.
There are animals that are not cats that have 4 paws,
so the inverse is false.
Cats have 4 paws, so the contrapositive is true.

23. If-Then Transitive Property
(postulate)
Given: If A, then B.
If B, then C.
Conclusion:
If A, then C.
(logic chain)

24. If yellow is
brown, then red is
blue.
If black is white, then
yellow is brown.
If red is blue, then
green is orange.

25. If black is white, then
yellow is brown.
If yellow is
brown, then red is
blue.
If red is blue, then
green is orange.

26. Write as a
conditional
ALL MATH
TEACHERS
ARE MEN.

27. WRITE IN IF-THEN
FORM.
IF A PERSON IS A
MATH TEACHER,
THEN THEY ARE
A MAN.

28. A VENN DIAGRAM
is sometimes used
in connection with
conditionals

29. If p , then q.
q
p

30. Make a Venn
diagram
If Ed lives in
Texas, then he lives
south of Canada

31. Venn Diagram
If Ed lives in Texas, then he lives
south of Canada.
Texas South of
Canada
Texas

32. Counterexample
If Ed lives south of Canada, then he
lives in Texas.
Texas
South of
Canada
Ed lives in
Maryland