12. Find the measure of angle M.
1. Draw and label line XY.
2. Draw and label plane QRS.
3. Draw line segment CD.
4. Determine whether the statement is true or false. Explain
your reasoning.
AB  CD, therefore their measures are equal.
M
5. True or False: Lines n, p, and m are coplanar.
13. Is A a proper name for the marked angle?
p
X
n
D
m
Y
W
C
E
V
K
B
T
Z
I
Q
A
G, K , H
G, I , H
G, H , J
H, I , G
F
G
L
F
[A] FEG, GEF, F
[B] FGE, GFE, E
[C] FGE, GFE, F
K
I
H
G
H
14. Name this angle in three different ways.
6. Which set of three points is noncollinear?
[A]
[B]
[C]
[D]
J
[D]  FEG,  GEF,  E
J
E
G
7. Write the symbol notation for the geometric figure. Then
name the figure.
C
15. SQ bisects RST. Find the measure of RSQ if
m RST  48 .
D
T
8. Name the line and plane.
Q
V
X
W
R
S
9. Find the coordinates of the point that lies one fourth of the
way from 6, – 10 to – 2, 12 .
b
g b
g
10. Determine which coordinates are the midpoints of the sides
y
of the quadrilateral.

16. Write a good definition for parallel lines. Explain which
words of your definition help differentiate the term.
17. Write a good definition for perpendicular lines. Explain
which words of your definition classify the terms.
18. Determine whether the following statement is true or false.
If it is false, explain why.
If Nancy does not drive a car, then she must walk to school.








19. Give a counterexample to the following statement.
 x
If a, b, c, and d are real numbers such that a > b
and c > d , then ac > bd .


b3, – 1g, b3, 1g, b– 3, 1g, b– 3, – 1g
[B] b– 1, 3g, b1, 3g, b1, – 3g, b– 1, – 3g
[C] b4, 0g, b0, – 4g, b– 4, 0g, b0, 4g
[D] b– 2, 2g, b2, 2g, b2, – 2g, b– 2, – 2g
[A]
11. Draw and label a 75° angle whose sides are UT and
20. Which is a counterexample to the definition below?
A rectangle is a figure with 2 pairs of congruent sides.
UV .
28. Based on the marks in the diagram below, which lines can
you assume to be perpendicular?
[A]
O
P
R
Q
[B]
[C]
[A] RO is perpendicular to OP and OP is perpendicular to
[D] There is no counterexample for this definition.
PQ
[B] RO is perpendicular to OP only
21. Which is a counterexample to the following faulty
definition?
A triangle is a figure with sharp corners.
[A] A square has four corners.
[B] Star shapes also have sharp corners.
[C] A triangle must have three sides.
[D] Lines are not considered figures.
[C] OP is perpendicular to PQ only
[D] cannot assume any lines are perpendicular
29. Based on the marks in the diagram below, which lines can
you assume to be parallel?
K
J
22. Draw a hexagon.
L
M
23. What name is given to polygons whose sides all have the
same length and whose angles all have the same measure?
N
O
24. Determine whether the figure below is a regular polygon. If
it is not a regular polygon, explain why.
[A] NO is parallel to
LM
[B] JK is parallel to
LM
[C] JK is parallel to NO
[D] cannot assume any lines are parallel
30. Based on the marks in the diagram below, which sides can
you assume to be congruent?
A
25. What is the perimeter of a regular hexagon if one of the
sides is 7 centimeters long?
C
26. Which is a concave polygon?
[A]
[B]
D
E
[A] AE  DC
[C] CE  AE
[B] CA  CE
[D] AE  AC
31. Classify BCD as equilateral, isosceles, or scalene.
[C]
C
[D]
8 cm
B
27. If quadrilateral ABCD is congruent to quadrilateral UVWX,
then BC is congruent to
.
9 cm
10 cm
D
32. Draw one triangle that is an isosceles triangle and also a
right triangle.
33. Classify the figure as quadrilateral, parallelogram,
rectangle, rhombus, square, or trapezoid. List all that apply.
38. Name the major arc and find its measure.
A
D
C
160
34. Name a radius of circle O below.
B
39. Identify a central angle.
D
EF is a(n)
35.
E
of circle O.
D
[A] DC
[B] DOC
O
[C] OC
[D] ACO
F
A
O
C
B
40. What are the dimensions of the solid shown below?
A
C
B
36. Identify two chords.
Q
R
U
41. What is the name of the solid shown below?
O
T
P
S
[A] RS and
TU
[B] PO and QO
[C] PQ and RS
[D] PQ and TU
37. In circle O, AB is a diameter and mBC  49 . Find
42. If the faces of the right trapezoidal prism in the figure below
were traced, how many rectangles and trapezoids would be
drawn?
m CAB .
C
A
O
B
43. On a second-grade camping trip, all the boys wanted to
sleep in one cabin that had a floor 24 feet wide by 50 feet long.
If each boy was assigned a 3- by 6-foot sleeping area and no
room was left over for one more sleeping area, how many boys
slept in the cabin?
44. Zadak is planting a circular garden. The garden is divided
into equal sections. Each section has a central angle of 20.
How many sections are there?
45. The chairs for a concert are arranged so that each row has
the same number of chairs. Christina has 5 seats in front of her,
and 9 behind her. There are 10 seats to her left and 9 to her
right. How many chairs are set up?
[A] 304
[B] 312
[C] 303
[D] 300
Complete each statement.
55. If two angles are vertical angles, then they are
.
56. If two angles are a linear pair of angles, then they are
.
46. Use inductive reasoning to find the next term in the
sequence, and explain the pattern used.
2, 20, 200, 2000,
57. If two angles are equal in measure and
, then each angle measures 90.
Use inductive reasoning to find the missing shape in each
pattern.
58. Find the measure of each lettered angle in the figure.
47.
48.
Find the nth term of the sequence.
49.
a
b
c
d
e
f 
g
h
j
59. Suppose you make the following conjecture: If two angles
are supplementary to the same angle, then they are congruent to
each other.
Find the nth term of the sequence.
50.
51. Describe a situation inside or outside school in which
deductive reasoning was used correctly.
52. How many two-person conversations are possible at a party
of n people? Of 150 people?
Complete the following deductive argument to show why the
conjecture is true:
Suppose A and B are both supplementary to C .
Then,
a. mA  mC 
and mB  mC 
Solve the first equation for mA.
b. mA 
Solve the second equation for mB.
c.
By substitution,
d.
.
Therefore, A  B by the definition of congruent angles.
53. Into how many parts do 50 concurrent lines divide the
plane?
54. In an 8-team floor-hockey league, each team plays each of
the other teams twice. What is the total number of games
played?
60. A math student draws 4 different triangles and measures
each of the three angles contained in the triangles. When she
adds up the angle measures in each triangle she gets a sum of
180 degrees. The student concludes that the sum of the angle
measures in every triangle add up to 180 degrees. Is this an
example of inductive reasoning? Explain.
61. A scientist observes that 5 of her 15 cactus plants grew in
the month of July and the remaining cacti did not. She
concludes, using inductive reasoning, that the month of July is
the growing season for her particular type of cacti. Is this a fair
conclusion to make? Explain.
62. Choose the correct rule for the sequence. Find the nth term
in the sequence if you know its term number is n.
Term
1
2 3
4
5
... n
Value – 4 1 6 11 16 . . .
[A
Multiply the term number by 6 and subtract 10; 6n  10
[B]
Multiply the term number by – 9 and add 5;  9n  5
[C]
Multiply the term number by 5 and subtract 9; 5n  9
68. There are thirty-two teams in a soccer tournament. Each
team plays until it loses 1 game. There are no ties. How many
games are played?
[A] 15 games
[B] 31 games
[C] 32 games
[D] 16 games
69. Draw the next figure. Complete a table and find the function
rule. Then find the 35th term. If you place 35 points on a piece
of paper so that no 3 points are in a line, how many line
segments are necessary to connect each point to all the others?
[D]
Multiply the term number by –10 and add 6;  10n  6
63. Find the rule for the nth figure. Then find the number of
colored tiles in the 200th figure.
70. If a polygon has a total of 560 diagonals, how many vertices
does it have?
[A] n n  3  280; there are 17 vertices
b g
nbn  3g
[B]
 560; there are 35 vertices
2
nbn  3g
[C]
 280; there are 17 vertices
2
[D] nbn  3g  560; there are 35 vertices
[B] n  8; 208
[D] n  2; 202
[A] 2n; 400
[C] 8n; 1600
64. Use the table and graph to write a linear function.
Term number n
bg
Value f n
1
2
3
4
5
13 21 29 37 45
71. Use deductive reasoning to write a conclusion for the pair of
statements.
All integers are rational numbers.
–2 is an integer.
f(n)
10
5
–10
–5
5
10 n
72. When you use _____ reasoning you are generalizing from
careful observation that something is probably true. When you
use _____ reasoning you are establishing that, if a set of
properties is accepted as true, something else must be true.
[A] deductive; inductive [B] inductive; deductive
[C] inductive; inductive
[D] deductive; deductive
–5
–10
73. Solve the equation for x. Give a reason for each step in the
process.
b
g b
g
3 2 x  1  2 2 x  1  7  42  5x
65. In a cupboard there are 15 loaves of bread. Seven of the
loaves are wheat bread. Half of the remaining loaves are white
bread. Of the remaining loaves, half are rye and half are
pumpernickel. How many loaves of white bread are there?
66. According to Miss Etiquette, there should be at least 11
inches of space or “elbow room” between people seated at a
dinner table. If the space that each person takes up is 2 feet not
including the elbow room, how many people can be
comfortably seated at a rectangular table that measures 88
inches by 63 inches?
67. After their meeting, each of the ten members of the Student
Nutrition Council shook hands with each other. How many
handshakes were there in all?
74. Use the true statement below and the given information to
draw a conclusion. Write that conclusion.
True statement: Two angles are complementary if the sum of
their measures is 90°
Given: A and B are complementary.
75. The definition of a parallelogram says, “If both pairs of
opposite sides of a quadrilateral are parallel, then the
quadrilateral is a parallelogram.” Quadrilateral LNDA has both
pairs of opposite sides parallel. What conclusion can you
make? What type of reasoning did you use?
[A] LNDA is a parallelogram; inductive
[B] LNDA is a rectangle; inductive
[C] LNDA is a parallelogram; deductive
[D] LNDA is a rectangle; deductive
76. Solve for x.
80. Find the unknown angle measures, given that lines l and m
are parallel.
b3x  127g
m
b4 x  4g

72°
a
93°
d
e
c
37°
b
56°
f
l
77. Solve for x.
81. Find x.

b5x  20g
b2 x  26g
b x  7g
b4 x  8g
78. Based on the marks in the diagram below, which angles can
you assume to be congruent?
A
B
C
F
82. What pair of lines are parallel if 4  12?
1 2
6 5
D
3 4
8 7
a
E
[A] BFA  DFE and BFD  AFE
[B] BAE and DEA
[C] C and DEA
[D] C and BAE
MM
MM
l m and j k . Name all angles
congruent to 8.
l
m
79. In the figure,
1 2
5 6
3 4
7 8
9 10
13 14
11 12
15 16
9 10
14 13
11 12
16 15
c
d
b
83. Is line l parallel to line m?
115
l
j
k
65
m
84. Find the slope of the line containing the points
and
b
g
b g
A 6, 9
B 9, 10 .
85. Graph the line that goes through the point
slope 
1
.
5
b4, 2g and has
[24] The figure is not a regular polygon because it is not
equiangular.
[25] 42 cm
[26] [C]
Answers:
[1]
X
Y
[2]
R
Q
S
[27] VW
[28] [A]
[29] [C]
[30] [D]
[31] scalene
[32] Sample answer:
[3]
C
D
[4] True. Congruent segments have equal measure.
[5] False. They do not lie on the same plane.
[6] [C]
[7] CD; ray
[8] line VW and plane VWX
[9]
FG 4,  9 IJ
H 2K
[10] [D]
[11]
T
V
[33] quadrilateral
[34] OU , OR, or OT
[35] tangent
[36] [C]
[37] 311°
[38] mADB  200
[39] [B]
[40] 5 units deep, 2 units wide, 4 units high
[41] cone
[42] 4 rectangles and 2 trapezoids
[43] 64 boys
[44] 18 sections
[45] [D]
[46] 20,000; Each number is 10 times the preceding number.
[47]
U
[12] 132
[13] Yes
[14] [D]
[15] 24°
[16] Sample answer: Parallel lines are lines in the same plane
that never meet.; The words “that never meet” differentiate
parallel lines from other types of lines.
[17] Perpendicular lines are lines that meet at 90 angles. The
words “lines that meet at 90 angles” are classifying the term
perpendicular lines.
[18] False; Sample answer: Nancy could take the bus to school.
[19] Sample answer: a = 0, b = –2, c = 2, and d = –4.
[20] [B]
[21] [B]
[22] Sample drawing:
[48]
[49] n + 7
[50] 5n – 3
[51] Answers will vary.
[52]
b g
n n –1
; 11,175
2
[53] 100
[54] 56
[55] congruent
[56] supplementary
[57] supplementary
[58] a  152 , b  28 , c  152 , d  76 , e  90 ,
f  118 , g  62 , h  62 , j  152
[23] regular polygons
[59] a. 180 ; 180
b. 180 – mC
c. mB  180 – mC
[75] [C]
d. mA  mB
[60] Sample answer:
This is an example of inductive reasoning because the math
student observed the same event in each triangle and
determined there was a pattern.
[61] Sample answer:
This is not a fair conclusion to make. The scientist has not
applied inductive reasoning. No growth pattern was found.
[62] [C]
[63] [C]
[64] f n  8n  5
[76] x  7
[65] 4 loaves
[66] 6 people
[67] 45 handshakes
[68] [B]
[80] a  71 , b  72 , c  52 , d  56 , e  87 ,
[69]
[81] x  5
bg
[77] x  2
[78] [A]
[79] angles 1, 3, 6, 9, 11, 14, 16
f  37
[82] a and b
Points 1 2 3 4
Lines
5 
0 1 3 6 10
b g
n
b g
n n 1
2

35
595
n n 1
; 595
2
[83] Yes
[84]
1
3
[85]
y
10
[70] [B]
5
[71] –2 is a rational number.
–10
[72] [B]
5
–5
[73]
b
b
b
–5
g b
g
g
g
3 2 x  1  2 2 x  1  7  42  5x
5 2 x  1  7  42  5x
5 2 x  1  35  5x
10 x  5  35  5x
10 x  30  5x
15x  30
x2
The original equation
Combine like terms
Subtract 7 from each side
Distribute
Subtract 5 from each side
Add 5 x to each side
Divide both sides by 15
[74] The sum of the measures of A and B is 90 .
–10
10 x