Name:
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Logic Review
Use the given phrase to create the stated form.
1. Complementary angles add up to 90°.
a. Conditional Statement:_______________________________________________
__________________________________________________________________
b. Converse: _________________________________________________________
__________________________________________________________________
c. Inverse: __________________________________________________________
_________________________________________________________________
d. Contrapositive: ____________________________________________________
__________________________________________________________________
2. Adjacent angles share a common side.
a. Conditional Statement:_______________________________________________
__________________________________________________________________
b. Converse: _________________________________________________________
__________________________________________________________________
c. Inverse: __________________________________________________________
__________________________________________________________________
d. Contrapositive: ____________________________________________________
__________________________________________________________________
Write the converse and a biconditional statement of the following:
3. If two lines are perpendicular then they intersect to form right angles.
a. Converse:_________________________________________________________
_________________________________________________________________
b. Biconditional:_____________________________________________________
_________________________________________________________________
4. If a point is a midpoint then it divides the segment into two congruent segments.
a. Converse:_________________________________________________________
_________________________________________________________________
b. Biconditional:_____________________________________________________
_________________________________________________________________
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Use p and q to write the symbolic statements in words.
5. p: today is Monday
q: tomorrow is Tuesday
a. q  p
b. ~p  ~q
c. p  q
d. p  q
e. p  q
6. Write a conclusion to each group of statements (if possible). State whether your
conclusion is based on the Law of Detachment, Law of Syllogism, or neither (invalid).
a) Virginia is north of Florida.
You are in Virginia.
Conclusion:
Law:
b) If you are a Junior at Freedom, then you drive a car.
You drive a car.
Conclusion:
Law:
c) If you drive 50 miles per hour in a school zone, then you will get a speeding ticket.
If you get a speeding ticket, then you will pay a fine.
If you pay a fine, you will be broke.
If you are broke, then you will not be able to go to the movies.
Conclusion:
Law:
7. Using the Law of Syllogism, write up a 5 statement argument that will conclude with the
following statement: “If you feed your dog, then you’ll be able to turn in your
homework”.
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Find a counterexample to disprove the conjecture.
8. The value of x – y is always less than the value of x.
_______________________
9. Supplementary angles always form linear pairs.
_______________________
10. The sum of two acute angles is always less than 90°.
_______________________
Name the property which each example represents.
11. For any angles A and B, if  A =  B, and  B =  C,
then  A=  C
12. XY ≅ XY
13. If AB + DE = BC + DC then AB = BC
________________________
________________________
________________________
14. According to the Symmetric Property of Angle Congruence, If  A ≅  B , then m  B
and m  A are_____________________________. (1pt)
a. Congruent
c. Linear
b. Supplementary
d. Complementary
15. Solve the Equation and write a reason for each step. (5pts)
a. 2(4x + 20 ) = 180
a. Original Equation (given)
b. ______________
b. Distributive Property
c. ______________
c.
d. ______________
d.
16. Based strictly on the diagram, which is a valid
conclusion?
a. No cat owners also own dogs.
b. No dog owners also own fish.
c. No fish owners also cats.
d. No pet owners own more than one pet.
17. Create a Venn diagram to illustrate the set relationship.
There are some students at Freedom High School that play football, basketball, and baseball,
some that just play one sport, and some that play two of the sports.
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A
B
D
C
18. Complete the proof.
Given: AB ≅BC, BC≅ CD, CD≅ AD
Prove: Perimeter of ABCD = 4AB
Statements
Reasons