This document contains a geometry drill with various geometry concepts and problems. It also contains a logic drill with conditional statements and vocabulary about conditionals. It discusses writing conditionals, their converses, inverses, and contrapositives. It provides examples of evaluating the truth value of these and using Venn diagrams to represent conditional statements.

1. Geometry Drill 10/10/14
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. Warm-Up

3. Review
For each transformation, or set of
transformations, determine the
mapping. Please be sure to show your
work for the multi-step mappings
1. Reflect over the line y = x
2. Translate along the vector <2, -3>
3. Reflect across the line x= 5, & then
translate along the vector <3, -4>

4. Pick a partner,
time to play a
game!
Must listen to the
instructions carefully!

5. Statements from the game
1. If you grew up in Baltimore Maryland,
then you have seen snow.
2. If you have seen snow, then you grew up
in Baltimore, Maryland.
3. If you are a twin, then you have a sibling.
4. If you have a sibling, then you are a twin.
5. If I am breathing, then I am sleeping.
6. If I am sleeping, then I am breathing

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

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

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

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

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

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

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

13. REVERSE THE
HYPOTHESIS &
CONCLUSION

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

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

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

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

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

19. 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.

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

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

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

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

24. Example 4: Biology Application
If an animal is an adult insect, then it has six legs.
Converse: If an animal has six legs, then it is an adult
insect.
No other animals have six legs so the converse is true.
Inverse: If an animal is not an adult insect, then it does
not have 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.

25. Check It Out! Example 4
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.
If an animal is a cat, then it has four paws.

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

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

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

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

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

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

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

34. If p , then q.
q
p

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

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

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