Chapter 2: Reasoning and Proof
1.]
Let p represent A is acute.
Let q represent B is acute.
Use the choices to create a symbolic representation of the following arguments. Write them in
the table below.
A is acute if and only if B is acute.
A is acute or B is acute.
Therefore, A is acute and B is acute.
p→q
2.]
Contrapositive:
p↔q
p  q
p q
∴p  q
If it is raining outside, then Patty will not go to the store.
Given the contrapositive, what is the original statement?
A]
If it is not raining outside, then Patty will not go to the store.
B]
If it is raining outside, then Patty will go to the store.
C]
If Patty goes to the store, then it is not raining outside.
D]
If it is not raining outside, then Patty will go to the store.
E]
If Patty does not go to the store, then it is raining outside.
∴p  q
3.]
The Venn diagram represents the set of cell phones in a store.



Let P represent the cell phones that take pictures.
Let I represent the cell phones that connect to the internet.
Let G represent the cell phones that have games.
Identify each region of the Venn diagram that represents the cell phones that only take pictures
and have games.
Cell Phones
I
G
4.]
Let m represent:
Angle A is obtuse.
Let n represent:
Angle B is obtuse.
P
What is a symbolic representation of the following argument?
Angle A is obtuse if and only if Angle B is obtuse.
Angle A is obtuse or Angle B is obtuse.
Therefore, Angle A is obtuse and Angle B is obtuse.
A]
m→n
m  n
B]
∴m  n
C]
m↔n
m  n
∴m  n
m→n
m n
∴m  n
D]
m↔n
m n
∴m  n
Chapter 3: Parallel and Perpendicular Lines
5.]
Transversal p cuts through lines a, b, c, d, and f. Identify all true statements by circling the
correct box(es).
line a // line b
line a // line c
line b // line c
line b // line f
line c // line f
line c // line d
6.]
Lines j and k intersect lines m and n in the image below. Identify each statement that could be
used to prove j // k and m // n by circling the correct box(es) below.
8 and 14 are supplementary and 8 ≅ 2
7 and 2 are supplementary and 8 ≅ 16
6 and 3 are supplementary and 3 ≅ 12
15 ≅ 11 and 4 and 11 are supplementary
4 ≅ 6 and 1 and 12 are supplementary
7.]
8.]
Line p contains the points (-4, 0) and (-2, 2). Line w is parallel to line p and passes through
the point (4, 1). Identify the points on line w by circling the correct box(es).
(-3, -6)
(-1, -3)
(5, 2)
(2, -2)
(1, 4)
(6, 3)
Lines a and b intersect lines c and d.
Which of the following statements could be used to prove that a // b and c // d?
A]
1 ≅ 6; 3 ≅ 5
B]
1 ≅ 6; 4 and 5 are supplementary
C]
1 ≅ 4; 1 and 2 are supplementary
D]
1 and 3 are supplementary; 1 and 6 are supplementary
9.]
Line t contains the points (-4, 7) and (5, -8).
Plot a point other than point P with integral coordinates that lies on a line that is parallel to t
and passes through point P.
10.]
Directions:
Write your answer in the box provided.
Line a passes through points with coordinates (-4, 5) and (2, -2).
What is the slope of a line perpendicular to line a?
Slope of perpendicular line =
Chapter 4: Congruent Triangles
11.]
Given:
Triangle WTR with WT = 13 and WR = 21.
Identify possible lengths for TR by circling the box(es) of your choice. You must circle all
correct answers.
12.]
Directions:
6
11
32
45
8
25
34
50
Circle the box to choose the ordered pair you want to select. You must circle all
correct answers.
The vertices of ∆ABC and the endpoints of ̅̅̅̅
𝐷𝐸 have integral coordinates. Identify all possible
ordered pairs for point F so that ∆ABC ≅ ∆DEF.
(-5, 4)
(2, 4)
(-5, -5)
(1, -5)
(-4, 5)
(1, 4)
13.]
Directions:
Complete the proof by filling in the blanks with the correct reasons given below.
Congruent segments are segments of equal
measure
AAS Triangle Congruence Postulate
SAS Triangle Congruence Postulate
Reflexive Property
Given:
Prove:
BC = 5;
EF = 5;
AB = 8;
DE = 8;
ABC = 60;
DEF = 60
∆ABC ≅ ∆DEF
Statements
Reasons
1. BC = 5; EF = 5; AB = 8; DE = 8;
ABC = 60; DEF = 60
1. Given
̅̅̅̅ ≅ ̅̅̅̅
̅̅̅̅ ≅ ̅̅̅̅
2. 𝐴𝐵
𝐷𝐸 ; 𝐵𝐶
𝐷𝐸
2.
3. ABC ≅ DEF
3. Congruent angles are angles of equal measure.
4. ∆ABC ≅ ∆DEF
4.
14.]
Directions:
Circle each answer you want to select. You must select all correct answers.
Two triangles are shown below on the coordinate plane.
Using coordinate methods and the information in the graph, identify each postulate that could
best be used to prove ΔCAB ≅ ΔDEF.
15.]
SSS Triangle Congruence Postulate
ASA Triangle Congruence Postulate
AAS Triangle Congruence Postulate
SAS Triangle Congruence Postulate
Given:
Triangle ABC with AB = 42 and BC = 20.
Which of the following are possible lengths for AC? Circle the box(es) of your choice. You
must select all correct answers.
12
20
22
32
42
50
62
70
16.]
Directions:
Write your answer in the box provided.
Two triangles are shown below on the coordinate plane.
Using coordinate methods, what three letters describe the best postulate that would prove
ΔCAB ≅ ΔDEF?
Triangle Congruence Postulate
17.]
Directions:
Write your answer in the box provided.
Look at the two triangles pictured below.
In order to prove these triangles congruent by the SAS triangle congruence postulate, angle B
needs to be proven congruent to –
Angle
18.]
Directions:
Complete the proof by filling in the blanks with the correct reasons given below.
Given:
Rectangle CBDF
Prove:
ΔDBC ≅ ΔCFD
Reflexive Property
Opposite sides of a rectangle are parallel
Side-Angle-Side (SAS) Postulate
Side-Side-Side (SSS) Postulate
Corresponding parts of congruent triangles are
congruent (CPCTC)
Opposite sides of a rectangle are congruent
Statements
Reasons
1. Rectangle CBDF
1. Given
̅̅̅̅ ≅ 𝐷𝐹
̅̅̅̅
̅̅̅̅ ; 𝐵𝐷
̅̅̅̅ ≅ 𝐶𝐹
2. 𝐵𝐶
2.
3. ̅̅̅̅
𝐶𝐷 ≅ ̅̅̅̅
𝐶𝐷
3.
4. ∆DBC ≅ ∆CFD
4.
19.]
Directions:
Write your answer in the box provided.
What value of x makes ∆STW ≅ ∆XYZ?
x=
20.]
Given the following diagram of a triangle, write in the angle measures and side lengths from
the given box that would make the triangle possible. (Figure not drawn to scale.)
21.]
Two sides of a triangle measure 9 inches and 13 inches. Write the numbers in the boxes that
would correctly represent the range of the third side of the triangle.
<x<
9
13
-4
11
4
21
5
22
22.]
The diagram is a map showing Jaime’s house, Kay’s house and the grocery store. Write the
segments that represent the distances from each place in order from least to greatest.
<
23.]
<
The vertices of ∆ABC and the endpoints of ̅̅̅̅
𝐷𝐸 have integral coordinates. Plot point F with
integral coordinates so that ∆ABC ≅ ∆DEF.
24.]
Write the reasons for the last three statements of this proof in the table below.
Given:
̅̅̅̅
̅̅̅̅ ≅ 𝑃𝑆
QSR ≅ TRS and 𝑃𝑅
Prove:
ΔQSR ≅ ΔTRS
Chapter 6: Similarity
25.]
Directions:
Circle the box to choose each value you want to select. You must select the two
correct values.
Identify the two values that will prove ∆CBA ~ ∆HGF.
5
26.]
8
25
56
Directions:
Write your answer in the box provided.
Given:
̅̅̅̅ // 𝐶𝐷
̅̅̅̅
𝐴𝐵
40
35
Based on the information given, which triangle similarity postulate could be used to prove
∆AEB ~ ∆CED?
triangle similarity postulate
27.]
Directions:
Write your answer in the box provided.
Consider the following terms:
Similar
Congruent
Equilateral
Right
If two angles of one triangle are congruent to two corresponding angles of another triangle,
these triangles can be considered –
28.]
For what value of x is ∆ABC ~ ∆DEF? Write your answer in the box provided.
x=
29.]
Given:
∆ACF is subdivided into smaller triangles
̅̅̅̅
𝐴𝐶 ⊥ ̅̅̅̅
𝐴𝐹 and ̅̅̅̅
𝐴𝐶 ⊥ ̅̅̅̅
𝐵𝐸 and ̅̅̅̅
𝐴𝐸 ⊥ ̅̅̅̅
𝐶𝐹
̅̅̅̅ and points D and E lie on 𝐶𝐹
̅̅̅̅
Point B lies on 𝐴𝐶
Based on the given information, identify two triangles that may NOT be similar.
30.]
Complete the proofs below by filling in the table.
Chapter 7: Right Triangles and Trigonometry
31.]
Directions:
Circle the box to choose each value you want to select. You must select all correct
answers.
Identify each group of segments that can form a right triangle.
7 in., 24 in., 25 in.
9 in., 40 in., 41 in.
24 in., 69 in., 74 in.
39 in., 52 in., 65 in.
8 in., 15 in., 19 in.
11 in., 60 in., 61 in.
30 in., 60 in., 68 in.
40 in., 42 in., 58 in.
32.]
Given:
Square ABCD
Identify all true statements by circling the box(es) you want to select. You must select all
correct answers.
If DB = 15, then BC =
15√2
If DB = √5, then BC =
2
√10
4
and DC =
15√2
and DC =
√10
2
4
If DB = 4√2, then BC = 4 and DC = 4
If DB = 14, then BC = 7√2 and DC = 7√2
If DB = √10, then BC = √5 and DC = √5
If DB = 4, then BC = √2 and DC = √2
33.]
Directions:
Write your answer in the box provided.
A ladder leans against a wall. The bottom of the ladder is 10 feet from the base of the wall, and
the top of the ladder makes an angle of 25 with the wall. Find the length, x, of the ladder to
the nearest foot.
34.]
Directions:
Choose the correct measurement for each statement and write it in the table.
Look at the image of a model building. Point A is 5 feet from the bottom of the model building.
Write each value correctly in the table below.
Statement
Measurement
The distance from point
A to the top of the
building (in feet).
The height of the
skyscraper (in feet).
√2
5
5√2
10
5
35.]
Directions:
Choose the correct measurement for each statement and write it in the table.
Consider the illustration of a ramp below. Place a measurement with each equivalent
statement.
Statement
Measurement
x
L (ft)
Cos (x)
H (ft)
Tan (x)
36.]
3√3
2√3
1
2
√2
2
3
2
45
60
√3
√2
Directions:
Write your answer in the box provided.
Two people stand on opposite sides of a river, as illustrated by the dotted lines in the diagram
below. Person #1 stands 20 yards away from a nearby tree, and Person #2 views the tree at an
angle of 60 degrees. To the nearest whole yard, how far is it from one side of the river to the
other side, d?
37.]
Directions:
Write your answer in the box provided.
The figure represents the side view of a rectangular frame for metal shelves. Two diagonal
braces support the frame. Round to the nearest whole number, what is the measure of x?
x=
38.]
This figure models a gate that has been constructed using two parallel vertical boards with a
diagonals board connecting them. Identify all of the statements that must be true by circling
the box(es) that you want to select. You must select all correct statements.
sinCAB + cosCAB = 180
sinCAB = cosCBA
CAB ≅ DAB
x2 + y2 = z2
̅̅̅̅
̅̅̅̅
𝐴𝐷 // 𝐶𝐵
Chapter 8: Quadrilaterals
39.]
Directions:
Circle the box to choose the answer you want to select. You must select all correct
answers.
Quadrilateral ABCD is a rectangle. If the coordinates for the given rectangle are A(-2, -2) and
B(1, 2), identify possible coordinates for C and D.
C(-1, 4) and D(-4, 0)
C(-3, 5) and D(-6, 1)
C(3, 0) and D(0, -4)
C(2, -1) and D(-1, -5)
C(5, -1) and D(2, -5)
40.]
Directions:
Circle the box to choose the polygon you want to select. You must select all
correct polygons.
Identify each regular polygon that could tessellate a plane.
Square
Pentagon
Triangle
Hexagon
Octagon
Decagon
41.]
Directions:
Circle the box to choose the answer you want to select. You must select all correct
answers.
Robert has made a mask consisting of two triangles and a regular hexagon. Identify all true
statements based on the image of Robert’s mask.
x = 72
x = 120
x = 132
y = 138
y = 162
y = 198
42.]
Given:
Quadrilateral ABCD
Which expression proves that ABCD is a rectangle?
A]
The length of each diagonal is √𝑟 2 + 𝑠 2
B]
The common midpoint of the diagonal is ( , )
C]
𝑠
̅̅̅̅ is − 𝑠
The slope of ̅̅̅̅
𝐴𝐶 is and the slope of 𝐵𝐷
D]
̅̅̅̅ and 𝐶𝐷
̅̅̅̅ is r and the length of both 𝐴𝐷
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ is s.
The length of both 𝐴𝐵
𝑟 𝑠
2 2
𝑟
𝑟
43.]
The figure shown is a regular hexagon.
What is the length of the diagonal AC?
44.]
A]
4√3 in.
B]
8 in.
C]
12 in.
D]
8√3 in.
The figure is composed of a regular pentagon and a rectangle.
What is the measure of each of the angles identified as x? Write your answer in box provided.
45.]
The diagonals of a rhombus are 10 and 24. Find the perimeter of the rhombus. Write your
answer in the box provided.
46.]
Find the length of the side of the parallelogram represented by 4x – 1. Write your answer in
the box provided.
Chapter 10: Properties of Circles
47.]
Directions:
Circle the box to choose a statement you want to select. You must select all
correct statements.
Given circle O, identify the true statements.
TRW = 98
SOT = 144
RWT = 130
ROT = 130
RTS = 43
ROS = 86
48.]
Directions:
Write your answer in the box provided.
A pizza with a diameter of 16 inches is cut into 10 equal sized pieces as shown below. An
engineer is asked to design a box to hold a single slice of pizza. What is the length of the crust,
x, of one slice of pizza? Round to the nearest inch.
inches
49.]
Directions:
Write your answer in the box provided.
A circular pizza has a diameter of 19 inches and is divided into 10 equal slices as shown. An
engineer is asked to create a box that hold 3 pizza slices. What should the minimum
measurement of the arc of the box, labeled x, to ensure it holds all of the slices? Round answer
to the nearest whole number.
inches
50.]
In circle O, mSOT = 68.
What is mSRT? Write your answer in the box provided.
mSRT =
51.]
Given:
Circle W
W(-4, 6)
Radius = 10 units
Which point lies on circle W?
52.]
A]
(0, 4)
B]
(2, 10)
C]
(4, 0)
D]
(6, 16)
Directions:
Circle the box to choose each statement you want to select. You must select all
correct statements.
A circular shaped tree has a measured circumference of 25 inches in 2010. The tree grows 1
inch in diameter each year afterwards and maintains the circular shape. In 2012, an arc is
permanently etched into a portion of the tree’s circumference, as illustrated below.
As the tree expands, the etched arc expands with it. Identify all true statements.
By 2027 the diameter will have more than tripled
since 2010.
The etched arc will never be longer than 1/6 of the
circumference.
In 2013 the radius will be more than 10 inches.
By 2018 the radius will have more than doubled
since 2010.
The etched arc will initially be just over 5 inches
in length.
In 2014, the ratio of the etched arc to the
circumference will be the same as it was in 2012.
53.]
Directions:
Circle the box to choose each statement you want to select. You must select all
correct statements.
A tree has a measured circumference of 15 inches in 2010. The tree grows ½ inch in diameter
each year. In 2012, two round stationary bars are drilled into the tree, as illustrated below.
Identify all true statements.
It will take more than 10 years for the
circumference to double.
The radius will double when the diameter
doubles.
If 𝜃 = 30 then the minor arc AB in 2012 will be
approximately 3 inches.
Sometimes during 2012, the circumference will be
exactly 16 inches.
The bars drilled into the tree are intersecting
tangents.
The angle 𝜃 will remain constant as the tree
expands.
54.]
Bob divides his circular garden into 10 congruent sectors to plant different types of flowers.
The circumference of Bob’s garden is 50.5 feet. What is the area of one sector of Bob’s garden?
55.]
Directions:
Circle the box to choose each sector you want to select. You must select all
correct sectors.
Given:
Circle R with diameter TA = 20 in. Identify two sectors that have a combined
area of about 36.1π sq in.
Sector 1
Sector 2
Sector 3
Sector 4
Sector 5
56.]
Directions:
Write the correct values in the table below.
The circle shown below has a center at point A where radius AC = 12 cm, CAD = 150 and
CAE = 60.
Measurement
Value (cm / cm2 )
The area of Sector Y
The length of minor arc CD
The area of Sector X
The length of minor arc CE
2π
4π
5π
10 π
12 π
24 π
30 π
60 π
57.]
Directions:
Write the correct values in the table below.
The circle shown below has a center at point A where radius AC = 8 cm, CAD = 135 and
CAE = 45.
Measurement
Value (cm / cm2 )
The area of Sector Y
The length of minor arc CD
The area of Sector X
The length of minor arc CE
1π
58.]
2π
Directions:
3π
4π
6π
8π
12 π
24 π
Write your answer in the box provided.
The circle shown below has a center at point A where the measure of DAC = 135 and the
radius AC = 7 cm.
What is the area of the shaded sector X, to the nearest whole number?
cm2
59.]
Directions:
Write your answer in the box provided.
The circle shown below has a center at point A where the measure of DAC = 150 and the
radius AC = 6 cm.
What is the area of the shaded sector X, to the nearest whole number?
cm2
60.]
Directions:
Circle the box to choose each equation you want to select. You must select all
correct equations.
Identify each equation that represents a circle with a diameter length of 16.
(x – 2)2 + (y + 8)2 = 64
(x + 8)2 + (y + 8)2 = 16
(x + 4)2 + (y + 4)2 = 16
(x – 1)2 + (y + 2)2 = 64
(x – 16)2 + (y – 16)2 = 8
61.]
Directions:
Circle the box to choose each point you want to select. You must select all
correct points.
A circle is defined by the equation (x – 4)2 + y2 = 9. Identify each point that lies on the circle.
(-5, 0)
(4, 9)
(1, 0)
(4, -9)
(4, 3)
(7, 0)
(4, -3)
(13, 0)
62.]
63.]
A]
35
B]
40
C]
45
D]
50
Circle O is defined by the equation x2 + (y – 2)2 = 25. Plot the center of circle O and one point
with integral coordinates that lies on circle O.
64.]
Given:
̅̅̅̅
Circle O with diameter 𝐶𝐷
C(-7, -4) and D(1, 2)
Create the equation of this circle using the options to the right.
65.]
Given:
Circle T with WP = 36 centimeters
What is the area of the shaded sector? Keep your answer in terms of Pi and write your answer
in the box provided.
cm2
66.]
Given:
Three concentric circles with the center O.
̅̅̅̅
̅̅̅̅ ≅ 𝐿𝑁
̅̅̅̅ ≅ 𝑁𝑂
𝐾𝐿
KP = 42 inches
Which is closest to the area of the shaded region?
67.]
A]
231 sq in.
B]
308 sq in.
C]
539 sq in.
D]
616 sq in.
Given:
Circle M with secants ⃗⃗⃗⃗⃗
𝐴𝐵 and ⃗⃗⃗⃗⃗
𝐴𝐶
mA = 30
If the length of arc BC is 3 cm, what is the circumference of the circle? Write your answer in
the box provided.
cm
68.]
69.]
The coordinates of the center of a circle are (-2, 6). This circle has a diameter of 10 units.
A]
What is the equation of the circle?
B]
Give the integral coordinates of two points that lie on the circle.
The equation of a circle is (𝑥 − 3)2 + (𝑦 + 4)2 = 16.
A]
What are the coordinates of the center of the circle?
B]
What is the radius of the circle?
C]
What is the diameter of the circle?
D]
Give the integral coordinates of two points that lie on the circle.
Constructions
70.]
71.]
72.]
Surface Area and Volume
73.]
Directions:
Circle the box to choose the answer you want to select. You must select all
correct answers.
Identify the cylinders with the same volume.
Cylinder A
Cylinder B
Cylinder C
Cylinder D
Cylinder E
74.]
A square pyramid has a surface area of 176 square inches and a lateral area of 112 square
inches. What is the value of x?
8 in.
16 in.
28 in.
32 in.
64 in.
75.]
Four various solids, not drawn to scale, and their respective measurements are illustrated
below. Arrange the solids, by name, from largest to smallest according to their surface area.
Prism
Sphere
Cylinder
Largest
76.]
Cone
Smallest
A cylinder has a volume of 300π cubic centimeters and a base with a circumference of 10π
centimeters. What is the height of the cylinder? Write your answer in the box provided.
cm
77.]
A cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. What
is the volume of a sphere with a radius equal to that of the cone? Write your answer in the box
provided.
cm3
78.]
Two cylinders, a sphere, and a cone are shown. Circle the two objects with the same volume.
79.]
A fish tank in the shape of a rectangular prism has these dimensions:



length = 20 inches
width = 10 inches
height = 12 inches
4
What is the volume of the water in the tank when it is full? Write your answer in the box
5
provided.
in3
Similar Solids
80.]
Directions:
Write the correct values in the table below.
An ice cube with equal side lengths melts but retains its shape. The ice cube’s side length is
compared at three different stages as it melts. The first stage represents the cube’s original side
measurement, before it melts. In the second stage, its side length melts to half of its original
length. During the third stage, the side length of the cube melts to a third of its length in the
second stage.
Complete the table with the correct ratios.
Comparison
Ratio
The volume of the ice cube in the 2nd stage to
the volume of the ice cube in the 3rd stage.
The volume of the ice cube in the 1st stage to
the volume of the ice cube in the 2nd stage.
Area of the base of the ice cube in the 1st stage
to the area of the ice cube’s base in the 2nd
stage.
Area of the base of the ice cube in the 3rd stage
to the area of the ice cube’s base in the 2nd
stage.
27
1
9
1
8
1
3
2
4
1
2
1
1
9
1
27
81.]
The ratio of the volume of two sphere is 64 : 27. What is the ratio of the length of the radii of
these two spheres?
A]
2:1
B]
3:4
C]
4:3
D]
4:9
E]
8:3
82.]
The ratio of the volume of two spheres is 8 : 27. What is the ratio of the lengths of the radii of
these two spheres?
83.]
If the height of a rectangular prism is decreased by , then which statement is true?
1
3
1
A]
The volume would decrease by .
B]
The volume would decrease by
1
C]
The volume would decrease by
1
D]
The volume would decrease by
3
6
9
1
27
84.]
Directions:
Write your answer in the box provided. Use “ / ” for fraction bar.
The diagonal of a cube is reduced to 25% of its original size. What fraction, in simplest form,
equals the ratio of the cube’s reduced volume to its original volume?
85.]
Directions:
Circle the box to choose each statement you want to select. You must select all
correct statements.
The radius of an enlarged right circular cylinder is four times the original measurement and the
height has been unchanged. Identify all true statements.
If the original radius is 5 inches, the new radius is 10 inches.
The volume of the enlarged cylinder is 16 times larger than the original volume.
The area of the enlarged base will be eight times larger than the area of the original base.
The volume of the enlarged cylinder is 4800 π cm3 if originally the radius was 5 cm and the height was
12 cm.
86.]
Directions:
Write your answer in the box provided.
The shape illustrated below is a square.
How many times larger will the area of the square be if each side is multiplied by 2?
times larger
87.]
Directions:
Write the correct values in the table below.
Spherical balloons A, B, and C are compared. Balloon B is 1/8 of the volume of balloon A.
Balloon C is 27 times the volume of balloon B. Complete the chart with the correct ratios.
Comparison
Ratio
The radius of balloon A to the radius of balloon B
The diameter of balloon B to the diameter of balloon C
The radius of balloon A to the radius of balloon C
The diameter of balloon C to the diameter of balloon A
2:1
88.]
Directions:
1:3
2:3
3:2
1:2
3:1
Write your answer in the box provided.
A trapezoid with a side measurement of 4 inches and an area of 15.6 square inches has been
enlarged to have an area of 39 square inches.
What is the new side measurement, x?
inches
89.]
Directions:
Circle the box(es) to choose each statement you want to select. You must select
all correct statements.
A stop sign is a typical regular octagon. The perimeter of a stop sign is tripled to increase
visibility. Circle all of the following that apply.
The area of the new sign will be 2 times as large as the original area.
The area of the new sign will be 9 times greater than the original area.
Any given diagonal of the new stop sign will be 3 times as long as the original diagonal.
Each side of the new stop sign will be 27 times as long as each side of the original stop sign.
90.]
Directions:
Write your answer in the box provided.
Gary opens up a snow cone business but only has one cup size that holds 8 ounces. He wants
to make a similar but much larger cup size that holds 16 ounces. How long should the
minimum diameter of the 16 ounce cup be if the diameter of the 8 ounce cup is 1 inch? Round
all measurements to the nearest hundredth.
inches
91.]
A company makes two similar cylindrical containers. The total surface area of the smaller
container is 0.81 times that of the larger container. The height of the larger container is 60
centimeters. What is the height of the smaller container?
A]
54 cm
B]
48.6 cm
C]
24.3 cm
D]
21 cm
92.]
Directions:
Circle the box(es) to choose each statement you want to select. You must select
all correct statements.
A skate ramp must be modified for safety reasons by cutting through the vertical dotted line
shown below and removing a piece of the ramp. The height of the ramp will shrink from 3 feet
to 2 feet.
Identify all of the statements listed below that are true.
The angle of incline (θ) of the ramp will be
steeper after modifying it.
The base length of the modified ramp will be 8
feet.
The length of the modified ramp will be between
8 and 9 feet.
The angle of incline (θ) of the ramp will be less
steep after modifying it.
93.]
Directions:
Type your answer in the box provided.
Below are two similar milk barrels.
The ratio of the volume of the largest barrel to the volume of the smallest barrel is 64 : 27.
What is the volume of the small barrel? Round your answer to the nearest whole number.
ft3
94.]
95.]
A rectangular prism has a volume of 36 cm3.
A]
If the height of the prism is tripled and the other dimensions do not change, what is the
volume of the new rectangular prism?
B]
If all dimensions of the original rectangular prism are tripled, what is the volume of the
new rectangular prism?
A cylinder has a surface area of 96 square inches. If all dimensions of this cylinder are
1
multiplied by to create a new cylinder, what will be the surface area of the new cylinder?
2
96.]
The heights of two similar triangles are in the ratio 2 : 5. If the area of the larger triangle is 400
square units, what is the area of the smaller triangle?
A]
64 square units
B]
160 square units
C]
1,000 square units
D]
2,500 square units
Transformations
97.]
Quadrilateral QRST is to be reflected over the line y = -x.
What are the coordinates of point T’ after this reflection?
98.]
A]
(-4, 2)
B]
(-2, -4)
C]
(2, 4)
D]
(4, -2)
Given:
Triangle ABC with vertices located at A(1, 1), B(2, -3), and C(-1, -4).
Triangle ABC will be reflected over the line y = x. What will be the integral coordinates of point
C’ after this transformation?
C’ (
,
)
99.]
In the design, a hexagon is inscribed in a circle.
Which point shows the location of Point Q after a 240 clockwise rotation around the center?
A]
S
B]
T
C]
U
D]
V
Symmetry
100.] What is the total number of lines of symmetry for this figure? Write your answer in the box
provided.