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Geometry Formulas
Area Formulas
Lateral Area of cylinder
 C  h  2 rh
Surface Area of prisms and cylinders  LA  2 B
 ph
1
Lateral Area of cone    p   r
2
1
Lateral Area of pyramid    p
2
Surface Area of pyramids and cones  LA  B
Lateral Area of prism
Surface Area of sphere
1
A(Triangle)  bh
2
1
A(Regular Polygon)  ap
2
1
A(Trapezoid)   b1  b2  h
2
A(Circle)   r 2
 4 r 2
A(Parallelogram)  bh
1
A(Kite & Rhombus)   d1  d 2
2
Volume Formulas
Volume of prisms
1
Bh
3
1 2
Volume of cones   r h
3
Volume pyramids 
 Bh
Volume of cylinders
  r 2h
Volume of sphere
4
  r3
3
Other Formulas
d
 x1  x2 y1  y2 
,


2 
 2
 x2  x1 2   y2  y1 2
m
C   d  2 r
y2  y1
x2  x1
a 2  b2  c 2
y  mx  b
y  y1  m( x  x1 )
Special Right Triangles
45
30
2x
x 3
x 2
x
1
60
x
45
x
ACP GEOMETRY – MIDTERM REVIEW
Chapter 1 Review Questions
1. Find the next two terms in the sequence:
a) 384, 192, 96, 48,
b) -4, -8, 24, 48, -144,
1 1 1 1
c)
, , ,
,
4 16 64 256
2. Which is the next figure in the sequence?
a)
b)
c)
d)
e) None of the above
3.
A
B
C
-5
10
x
If AC= 36, then x = ________
4.
-3
17
The distance between the two points is ______.
5. Identify what each of the following means:
a) AB
____

b) AB
c) AB

d) AB
6. Find a counterexample to show that each conjecture is false:
a) A number squared is greater than the number.
b) The difference of two positive integers is positive.
2
7. Use the figure to answer the questions:
a)
b)
c)
d)
e)
Name two collinear points
Name two lines that intersect at point B.
Name three planes that intersect at point F.
Name two planes that do not intersect.
Name four points that are not coplanar.

f) Plane EFGH and CH intersect at __________.
8.
T
R
U
m
S
Y
a)
b)
c)
d)
X
V
Name a line segment.
Name a pair of opposite rays.
Name line m three different ways.
Name 2 lines which appear parallel.
9. a) M is a point on segment GS,
between G and S.
GS = 32
GM = 3x+10
MS = x-2
Find: x, GM, MS
b) G is the midpoint of
segment LS.
LG = 6x+5
GS = 2x +9
Find x, LS, GS, LG
10. a. Name 1 two other ways.
b. If m 1 = 142°, find m 2
c.  KJT and  TJF are ______________.
d. If m 2 = 5x+2 and m 1 = 24x+2, find x.
T
1
3
F
J
2
K
11. Use the points below to answer the following questions
A (0,3) B (-1, -4)
C(-7.-9)
D (8,10)
E (0. -2)
Find: a) AE
b) BC
c) midpoint of segment BE
d) midpoint of segment CD
12. The midpoint of segment QT is (-5, 1). The coordinates of point Q are
(-7,4). Find the coordinates of point T.
13. Find the area of the region:
a)
6
b) Radius of larger circle = 4
Radius of smaller circle = 2
3
3
8
2
Find the area of the ‘donut’
14. Find the perimeter of a four sided figure with the following vertices:
A (-4, 5), B(3, 5), C(5, -2) and D(-4, -2).
4
Chapter 2 – Midterm Review
Identify the hypothesis and conclusion of each conditional statement.
1. If a figure is a rectangle, then it has four right angles.
2. If an integer ends with 0, then it is divisible by 5.
Write each sentence as a conditional.
3. A square has four sides.
4. All obtuse angles have a measure greater than 90.
Show that each conditional is false by finding a counterexample.
5. If the name of a state contains the word New, then the state borders an ocean.
6. If an odd integer is less than ten, then the integer is prime.
Write the converse of each conditional statement, and determine the truth value of both
statements.
7. If you are in Indiana, then you are in Indianapolis.
8. If a point is in the first quadrant, then its coordinates are positive.
Use the given property to complete each statement.
15. Addition Property of Equality: If 2x  5  10 , then 2x = _____.
16. Subtraction Property of Equality: If 5x  6  21, then ______ = 15.
17. Symmetric Property of Equality: If AB = YU, then _____ = _____.
18. Symmetric Property of Equality: If H  K , then _____  H .
19. Reflexive Property of Equality: PQR  _____.
20. Distributive Property: 3( x  1)  _____.
5
21. Substitution Property: If LM = 7 and EF + LM = NP, then _____ = NP.
22. Transitive Property of Congruence: If XYZ  AOB and AOB  WYT , then _____.
23. Multiplication Property of Equality: If
1
TR  UW , then _____.
3
If the conditional and its converse are true, write a biconditional statement.
24. If a point is a midpoint of a segment, then the point divides a segment into two congruent
segments.
25. If two lines are parallel, then the two lines do not intersect.
Use the figure to identify the following.
A
26. an angle supplementary to AOD
B
27. an angle adjacent AND congruent to AOE
E
28. an angle supplementary to EOA
O
29. an angle complementary to EOD
D
30. a pair of vertical angles
C
Find the value of the variables.
31.
32.
(7 x  3)
65
(4 x  1)
(4 y )
(6 y )
6
Chapter 3 Midterm Review
1) Find m1 and then m2. Justify each answer.
2) Find the value of x. Then find the measure of each angle.
3) Find the value of x. Then find the measure of each angle.
4) Find the value of x for which a||t.
7
5) Find the value of x for which a||t.
6) Find the value of x for which a||t.
7) Find the value of x for which a||t.
8
8) Find the value of each variable.
9) Use a protractor and a ruler to measure the angles and sides of the triangle.
Classify the triangle by its angles and sides.
10) Find the values of the variables for the regular polygon below.
9
11) Find the missing angle measures
12) What is the interior angle sum of a convex 22-gon?
13) What is the measure of an exterior angle of a regular 13-gon?
14) The measure of an interior angle of a regular polygon is 135. Find the
number of sides.
Use the Coordinate Plane below to graph #15-17.
15) Graph 3x + 9y = 18 using slope-intercept form.
16) Graph x = -2.
17) Graph y = -5.
10
18) Write an equation of the line containing points A(2,7) and B(3,4).
19) Are the lines parallel, perpendicular or neither? Explain.
y  3x  2
y
1
x2
3

Chapter 4
1) If ΔHIL  ΔSUV name the corresponding angles and sides. (Sections 4-1)
2) Supply the reasons in this proof (Sections 4-2)
__
__
Given: X is the midpoint of AG and of NR.
Prove: ΔANX  ΔGRX
A
Reasons
R
1
X
2
a)
Statements
__
X is the midpoint of AG
N
G
b)
c)
<1  <2
__
__
AX  GX
__
d) X is the midpoint of NR
___ ___
e)
NX  RX
f) ΔANX  ΔGRX
11
In #3 - 8 state which postulate, if any, could you use to prove the tow triangles congruent? If not
enough information is given, write not possible. (sections 4-2, 4-3, 4-6)
3)
4)
6)
5)
7)
8)
In #9 – 10, find the values of the variables (section 4-5).
9)
10)
x
100
x
50
110
y
y
11- 12) Prove using a two column proof . (Section 4-6 and 4-7)
11)
__ __ __
__
__
__

Given: JL  LM, LJ  JK, and MJ KL
Prove: ΔMJL  ΔKLJ
M
L
12
J
K
12)
__
Given: FE
__
Prove: GE


__
GH and <GHE  <FEH
__
FH
G
F
M
E
Chapter 5
1. In GIK , the points H, L, and J are midpoints.
HL = 7, HJ = 6, and GI = 13.5
Find GK =_________ LJ = _________ IJ = ___________
2. In IKM , the points J, L, and N are midpoints.
JO = 15, KQ = 32, and IL = 33
Find JM= _______, LQ = _________, KN = ________
13
H
3. Use the diagram to answer the following questions.
a. How is EM related to HEK ?
b. Find the value of y, then find mMEL .
c. Find IK.
d. What can you conclude about point I?
4. AC is the perpendicular bisector of BD . If AB =12 and CD = 13, Find CB=______AD=_____
5. In the diagram, points F, B, D, G, H, I are midpoints. If IH = 7 , AE = 28, AB = 8, and GH = 4.
Find: GI =______, EC =______, FI = _______, AC =_________
6. In the diagram, K, O, and M are midpoints. Find the value of x.
14
7. A triangle has one side of 13 cm. and another side of 9 cm. What are the possible lengths of the
third side of the triangle? (show your work)
8. Can segments with lengths of 42.5 in., 16.5 in. and 25.9 in. form a triangle? (show your work)
9. List the angles of BCD from smallest to largest if BC = 27, CD = 29, and BD = 8
10. List the sides of BCD from largest to smallest if mB  72 , mC  59 , and mD  49 .
Chapter 8
1. Given
ABC
DEF .
Find the value of x.
Are the following triangles similar? If so, give a reason and write a similarity statement.
B
A
2.
80
36
64
E
C
64
D
3.
F
N
M
12
6
P
15
Q
R
28
15
S
4. List the ways you can prove two triangles similar.

5. EKN is similar to OHT . If mK  49 and mT  73 , find mE .
6. Solve the following proportion:
x 1 x  2

3
6
7. A scale model of a new school shows the tables to be 6 in long. The actual tables will be 72
inches long.
Find the ratio of the length of the model to the length of the actual table.
8. Find the geometric mean of the following, rounded to the nearest tenth.
a) 6 and 18
b) 7 and 125
c) 9 and 36
9. LUV is similar to GEO . The perimeter of LUV is 45 in. The perimeter of GEO is 105
in.
Find:
a) their similarity ratio
b) the ratio of their areas
10. Two figures are similar with a similarity ratio of 4 : 5 . The area of the larger figure is 475 in 2 .
Find the area of the smaller figure.
11. The triangles are similar. Find the missing side(s) in each figure.
16
12. The triangles are similar. Find the missing side(s) in each figure.
For #13 – 15, the triangles are similar. Find the missing lengths.
13.
14.
15.
16. At a golf course, Maria drove her ball 192 yd straight toward the cup. Her brother Gabriel
drove his ball straight 240 yd, but not toward the cup. The diagram shows the results. Find x and y,
their remaining distances from the cup.
CUP
x
G
y
M
START
17. Joan places a mirror 24 ft from the base of a tree. When she stands 3 ft from the mirror, she can
see the top of the tree reflected in it. If her eyes are 5 ft above the ground, how tall is the tree?
(Draw the situtation described and explain why the triangles are congruent)
17
Find the missing values.
18.
19.
20.
18
ACP Geometry – Midterm Review ANSWERS
Chapter 1
1a. 24, 12
1b. -288, 864
1c.
1
1
,
1024 4096
2. C
3. 31
4. 20
5a. length of the segment from A to B
5b. segment from A to B
5c. line containing points A and B
5d. ray with endpoint at A and goes through B
6a. 0, 1
6b. 3  7
7&8. Multiple Answers
9a. x = 6, GM = 28, MS = 4
9b. x = 1, GS = 11, LG = 11, LS = 22
10a. TJF and FJT
10b. 38
10c. Adjacent and Supplementary
11a. 5
11b. 61  7.8
11c. (0.5, 3)
12. ( 3, 2)
13a. 39
13b. 12  37.68
14. 7  7  9  53  7  7  9  7.2  30.2
10d.
176
 6.067
29
11d. (0.5, 0.5)
Chapter 2
1. H = a figure is a rectangle
C = it has four right angles
2. H = an integer ends with 0
C = it is divisible by 5
3. If a figure is a square, then it has four sides.
4. If an angle is obtuse, then it has a measure greater than 90.
5. New Mexico
6. 9
7. If you are in Indianapolis, then you are in Indiana.
Conditional = False
Converse
= True
8. If a point has coordinates that are positive, then it is in the first quadrant.
Both True
15. 15
16. 5x
17. YU = AB
18. K
19. PQR
20. 3x – 3
21. EF + 7
22. XYZ  WYT
23. TR  3(UW )
24. Biconditional: A point is a midpoint of a segment iff it divides a segment into two congruent
segments.
25. Not possible b/c converse can be skew lines.
26. AOB or DOC
19
27. EOC
28. EOC
29. DOC
30. DOC & BOA or BOC & DOA
31. x = 16
32. y = 9
Chapter 3
1) m1 = 100 Alternate interior. m2 = 100 Alternate interior or vertical
2) x = 103, 77, 103
3) x = 30, 85, 85
4) 43
5) 38
6) 100
7) 48
8) v = 118, w = 37, t = 62
9) obtuse isosceles
10) n = 360/7 = 51.43
11) x = 129
12) 3600
13) 27.69
14) 8
15) slope = -1/3, y-intercept at 2
16) Vertical line at x = -2
17) Horizontal line at y = -5
18) y = -3x + 13
19) Neither…3 does not equal 1/3…3 times 1/3 does not equal –1.
Chapter 4
1. Sides: HI=SU, IL=UV, LH=VS
Angles: H=S, I=U, L=V
2. a. Given, b. Vertical Angles, c. Def. of midpt.,
d. Given, e. Def of midpt., f. SAS
3. ASA or AAS 4. AAS or ASA
5. SSS 6. not possible 7. HL 8. SAS
9. x=40 y=70
10. x=80 y=40
11. and 12.  your discretion
Chapter 5
1. GK=12 LJ=6.75 IJ=7
2. JM=45 LQ=11 KN=48
3. a) Angle Bisector b) y=11, 66
c) 18.5 d) I is on Angle Bisector
20
4. CB=13 AD=12
5. GI=7 ED=28 FI=4 AC=16
6. x=14
7. 4<x<22
8. No
9. C, D, B
10. CD, BD, BC
Chapter 8
1. x=20
2. yes, AA~ 3. No 4. AA~, SAS~, SSS~
5. 58 6. x=4
7. 1:12
8. a) 10.4 b) 29.6 c) 18
9. a) 3/7 b) 9/49
10. 304 sq. in.
11. x=13.5 y=20.25
12. x=3.4 y=4.47
13. x=28
14. x=1.78
15. y=7.2
16. x=180 y=108
17. 40 ft
18. y=7.5
19. x=6
20. a=4.5 b=7.5
21