Geometry
Review Sheet
Name_________________
A. Name or state the property, postulate, theorem, or definition that justifies each statement.
3. If AOB is a right , then OA
5. If a + 7 = 4, then a = -3.
7. If
RS  ST
#7-8
2. If K  L and L  M, then K  M.
1. If 8x = 16, then x = 2.
 OB .
, then S is the midpoint of
V
4. If a + 7 = b and b = 4, then a + 7 = 4.
6. W is between M and N, MW + WN = MN.
RT
. 8. If
SW
R
S
W
T
bisects VST, then VSW  WST.
B. Classify each as True or False. If False, provide a counterexample.
2.  lines form  adjacent ’s.
4. Complementary ’s must be adjacent.
6. Supplementary ’s must form a linear pair.
1. Through any 3 points there is exactly one plane.
3. Vertical angles are always supplementary
5. Supplements of  ’s are always .
C. In the diagram,
1.
2.
3.
4.
5.
OB
bisects AOC and
EC  OD .
Find the value of x.
#1-5
B
A

m5 = 2x, m4 = x + 60
m1 = 2x, m2 = 6x + 2
m2 = 6x + 9, m5 = 2x + 49
m1= 3x, m2 = 2x +10
m3 = x – 9, m4 = 2x + 5, m5 = 3x – 26
E

4 5
O
3
2

C
1
D
Z 
#6-7
6. If BOC is a right  and mCOD = 58, then
m  DOE = ____, m BOA = _____, and mAOC = _____.
B
7. Name a supplement of AOE.
E
O
A
8. A supplement of a given angle is four times as large as a complement
of the angle. Find the measure of the given angle.
9. Point M is the midpoint of
RT
D
. RM = x and RT = 4x – 6 . Find x.
10. Name 3 angles that have vertex D.
Which angles with vertex D are adjacent?
a) mCBD = ______ b) Name the postulate that you used in a)
11. What kind of angle is CBD?
12.
D
C
BD bisects ADC, m1 = 5x – 3 and m2 = x + 25,
# 10-12
88
A
find x.
13. m1 = 3x –5 and m2 = x + 25. Find x and m1.
For 14 and 15 you are given that OB  l and OA
14. If m3 = 37,
m4 = _____, m5 = _____, m6 = _____
1 2
#13
 OC .
C
B
2
1
#14-15
l
A
6
15. If m5 = 35
m3 = _____, m4 = _____, m6 = _____
O
3
II. Algebra Must define variables and show algebra!
5
4
B
C
1
15. C and D are complementary. If mC = x + 10 and mD = 2x – 7, find x, mC, mD.
16. A and B are supplementary. If mA = x2 and mB = -3x + 110. Find x, mA, mB.
17. The measure of a complement of an angle is 20 more than the measure of the angle. Find the measure of the angle.
18. The measure of a supplement of an angle is five times as large as the measure of the angle. Find the measure of both angles.
19. The difference between the measures of two supplementary angles is 30. Find the measure of the smaller angle.
III. Logic
20. Given: If you graduated from Duke then you are not a fan of football season.
Converse:
Inverse:
Contrapositive:
21. Give a counterexample for:
If 2 ’s are supplementary then they form a linear pair.
22. Given: B is midpoint of AC
●
A
D is midpoint of CE
Prove: AB + CD  BC  DE
Statements
1) B is midpoint of AC
Reasons
1)
D is midpoint of CE
2) AB  BC
3)
CD  DE
AB  BC
CD  DE
4) AB +
CD  BC  DE
2)
3)
4)
2
●
B
●
C
●
D
●
E