Download Lesson 1: Measurement and Geometry

Lesson 1: Measurement and Geometry
Directions: Read each question carefully and then choose the best answer.
Use the diagram below to
answer question 1.
Use the pictures below to
answer question 3.
3. Which pair of code symbols
is representative of a rotation?
A.
1. What is the total area of both
triangular fins of the rocket?
A.
B.
C.
D.
54 square feet
108 square feet
216 square feet
270 square feet
2. The garden club put in two
rotating sprinklers, each of
which waters a circular area of
10 meters in diameter. What is
the approximate total area that
the two sprinklers will water?
J.
K.
L.
M.
78.5 square meters
157 square meters
314 square meters
628 square meters
ACES Mathematics: Geometry Workbook
B.
C.
D.
Use the picture below to
answer question 4.
4. How many buckets of sand
will it take to fill the sandbox
below if each bucket contains 2
cubic meters of sand?
J.
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M.
12
13
16
32
1
Lesson 2: Principles of Geometry I
Directions: Read each question carefully and then choose the best answer.
1. What is the perimeter of a
rhombus with one side that is 5
inches long?
A.
B.
C.
D.
15 inches
20 inches
25 inches
30 inches
3. Triangles ABC and DEF are
similar. If AB = 4, BC = 2, AC =
5, and DE = 3, what is the
perimeter of triangle DEF?
B
A
2. In the figure below, a triangle
is inscribed in a parallelogram.
The base of the triangle and the
base of the parallelogram are
equal. If the area of the
parallelogram is 16, what is the
area of the triangle?
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C
E
D
F
A.
8
B.
C.
10
11
D.
16
1
4
7
8
8
10
12
It cannot be determined.
ACES Mathematics: Geometry Workbook
2
Lesson 3: Principles of Geometry II
Directions: Read each question carefully and then choose the best answer.
1. Which letter has line
symmetry?
A.
B.
C.
D.
F
H
J
P
2. In the figure below, a black
triangle is completely contained
but not inscribed in a rectangle
as shown. If the area of the
rectangle is 20, which of the
following must be true?
3. The rectangle below is
divided into four triangles by its
two diagonals. The dimensions
of the rectangle are 14 inches by
8 inches. What is the area of the
black triangle?
A.
B.
C.
D.
14 square inches
28 square inches
42 square inches
56 square inches
Note: The figure is not drawn
to scale.
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M.
The area of the triangle is
more than 20.
The triangle must be
irregular.
The area of the triangle is
less than 10.
The perimeter of the
rectangle is less than 18.
ACES Mathematics: Geometry Workbook
3
Lesson 4: Principles of Geometry III
Directions: Read each question carefully and then choose the best answer.
1. Which of the letters below
has rotational symmetry?
A.
B.
C.
D.
E
H
L
Q
2. In the figure below, l1 is
parallel to l2 and l3 is parallel to
l4. The obtuse angle formed by
l1 and l4 measures 140º, as
shown in the diagram. Line
segment BC bisects ABD .
l3
C
l4
3. A large-scale map uses the
figure shown above, which is
made up of a square and an
isosceles triangle sharing one
side, to represent houses in the
community. The height of the
triangle is ½ the height of the
square. If the square in the
diagram has sides of 1 inch,
what is the area, in square
inches, of the entire figure?
A. 1 square inch
D
A
B.
140º
B
l1
l2
C.
D.
What is the value of ABC ?
J.
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M.
40º
70º
120º
140º
ACES Mathematics: Geometry Workbook
1
square inches
4
1
1 square inches
2
1
2 square inches
4. The length of the third side of
any triangle must be greater than
J.
the length of either of the
other two sides.
K. the product of the lengths
of the other two sides.
L.
the sum of the lengths of
the other two sides.
M. the difference between the
lengths of the other two
sides.
4
Lesson 5: Problem Solving with Geometry I
Directions: Read each question carefully and then choose the best answer.
Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and
plot the points identified in the problems.
1. A circle plotted on a
coordinate grid has its center at
(0, 0). The radius of the circle is
4. Through which of the
following points does the
circumference of the circle pass?
A.
B.
C.
D.
(2, 2)
(–4, 0)
(4, 4)
(4, –4)
2. A triangle plotted on a
coordinate grid has vertices at
coordinates (4, 1), (12, 1), and
(4, 4). What is the area of the
triangle?
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J.
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6
9
12
18
ACES Mathematics: Geometry Workbook
12
16
24
48
5. Square S and right triangle T
share a side, as shown in the
diagram below. If the area of
triangle T is 6 square inches,
what is the area of square S?
8
12
24
48
3. A triangle plotted on a
coordinate grid has vertices at
coordinates (0, 0), (3, 3), and
(6, 0). What is the area of the
triangle?
A.
B.
C.
D.
4. A rhombus on a coordinate
grid has vertices at coordinates
(0, 0), (3, 4), (6, 0), and (3, –4).
What is the area of the
rhombus?
S
T
3 in.
A.
B.
C.
D.
4 square inches
6 square inches
8 square inches
16 square inches
5
Lesson 6: Problem Solving with Geometry II
Directions: Read each question carefully and then choose the best answer.
Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and
plot the points identified in the problems.
1. Line segment AB has
endpoints at (–2, –2) and (6, 4).
What is the midpoint of this line
segment?
3. What is the area of a
quadrilateral with vertices at
points (–5, –1), (–2, 3), (6, –1),
and (–2, –5)?
A.
B.
C.
D.
A.
B.
C.
D.
(1, 2)
(2, 1)
(–2, 4)
(6, –2)
2. A triangle plotted on a
coordinate grid has vertices at
coordinates (2, 4), (14, 4), and
(14, 9). What is the area, in
square units, of the triangle?
J.
K.
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M.
13
30
60
126
ACES Mathematics: Geometry Workbook
10
11
30
44
4. What is the perimeter of a
quadrilateral with vertices at
points (–5, –1), (–2, 3), (6, –1),
and (–2, –5)?
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52 5
54 5
10  4 5
10  8 5
6
Lesson 7: Problem Solving with Geometry III
Directions: Read each question carefully and then choose the best answer.
Hint: You may find it helpful to create a coordinate grid on a piece of graph paper and
plot the points identified in the problems.
1. What is the area of a triangle
with vertices at (–2, 5), (–2, –1),
and (3, –1)?
4. What is the midpoint of a line
segment with endpoints (–8, –6)
and (–1, –6)?
A.
B.
C.
D.
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5
10
15
30
2. What is the perimeter of a
triangle with vertices at (–1, 1),
(–1, –5), and (2, –5)?
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9  10 2
12
25
2
93 5
(–3.5, –6)
(–4.5, –6)
(–3.5, –3)
(–4.5, –3)
5. What is the area of a
quadrilateral with vertices at
points (–3, 0), (0, 4), (3, 0), and
(0, –4)?
A.
B.
C.
D.
6
12
18
24
3. What is the area of a triangle
with vertices at (2, 5), (8, 5), and
(2, 3)?
6. What is the perimeter of a
quadrilateral with vertices at
points (–3, 0), (0, 4), (3, 0), and
(0, –4)?
A.
B.
C.
D.
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M.
6
9
15
18
ACES Mathematics: Geometry Workbook
48
24
20
14
7
Lesson 8: Circles
Directions: Read each question carefully and then choose the best answer.
1. The drawing below shows an
isosceles triangle with one
vertex at the center of the circle
and the other two vertices on the
circumference of the circle. If
the length of each leg of the
triangle is 2, what is the area of
the circle?
A.
B.
C.
D.
3. The radius of circle A is
twice the radius of circle B. The
area of circle A is how many
times larger than the area of
circle B?
A.
B.
C.
D.
2
4
8
It cannot be determined.
4. The diagram below shows
two circles, each with a radius of
2. The circles are tangent to each
other. Each is inscribed in the
rectangle.
6
4
2

A
B
2. Chords w, x, y, and z transect
circle C as shown in the diagram
below. Which chord is longest?
w
What is the area of the
rectangle?
x
C
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M.
y
z
w
x
y
z
ACES Mathematics: Geometry Workbook
J.
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M.
4
8
16
32
8
Lesson 9: Angle and Distance Measures
Directions: Read each question carefully and then choose the best answer.
1. In triangle ABC below, side
AB < side BC < side AC. Which
answer choice gives the correct
order of the angle values a, b,
and c?
3. An isosceles right triangle
has a hypotenuse of 6 2 . What
is the area of the triangle?
A.
B.
C.
D.
B
bº
aº
cº
A
A.
B.
C.
D.
C
18
36
72
144
Use the figure below to answer
question 4.
a<b<c
b<c<a
c<b<a
c<a<b
C
yº
xº
2. What is the sum of the
interior angles of the polygon
shown below?
yº
xº
A
yº
B
D
4. In the figure, line segments
AB and CD meet to form two
right angles. What is the value
of x – y?
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360º
540º
720º
900º
ACES Mathematics: Geometry Workbook
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0
15
30
45
9
Lesson 10: Coordinate Geometry
Directions: Read each question carefully and then choose the best answer.
Use the coordinate grid below
to answer questions 1 and 2.
Hint: To answer questions 3 and
4, you may find it helpful to
create a coordinate grid on a
piece of graph paper and plot the
points identified in the
questions.
3. Point Z has coordinates
(5, 9). If Z is reflected across the
y-axis, then translated down 7
units, what are the coordinates
of the resulting point?
1. The coordinates of point A
are (1, 1) and the coordinates of
point B are (7, 9). What is the
slope of AB?
A.
B.
C.
D.
–1
3
4
1
4
3
2. What is the length of AB?
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A.
B.
C.
D.
(–2, 2)
(–5, 2)
(–5, –2)
(–5, –16)
4. If point Z (5, 9) is reflected
across the y-axis and the result is
reflected across the x-axis, what
are the coordinates of the
resulting point?
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M.
(–5, –9)
(–9, –5)
(5, –9)
(–9, 5)
2
10
14
18
ACES Mathematics: Geometry Workbook
10
Lesson 11: Theorems with Geometry I
Directions: Read each question carefully and then choose the best answer.
1. If l1 is parallel to l2, which
angles are congruent in the
diagram below?
a
l1
A.
B.
C.
D.
d
b
e
l2
c
A.
B.
C.
D.
3. Which parts of two triangles
must be congruent in order to
show that the two triangles are
entirely congruent?
f
a and b
b and c
a and d
d and f
one side
two angles
one side and one angle
two sides and the angle at
which those sides meet
4. Side BC of rectangle ABCD
is congruent to side EF of
rectangle EFGH. If ABCD and
EFGH are similar rectangles,
what is the perimeter of
rectangle EFGH?
2. In triangle ABC below,
a 2  b 2  c 2 only if
6
A
A
3
c
b
B
D
C
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a
B
ACB = 90º
AC = BC
ABC and CAB are
supplementary
ABC = CAB
ACES Mathematics: Geometry Workbook
J.
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M.
C
E
F
H
G
6
9
12
18
11
Lesson 12: Theorems with Geometry II
Directions: Read each question carefully and then choose the best answer.
3. In the figure below, l1 is
parallel to l2. What is the value
of x?
A
C
B
x
l1
F
x
( )
5
H
G
1. Triangles ABC and FGH are
similar triangles with
corresponding parts as shown in
the diagram. ABC is equal to
which angle in triangle FGH?
A.
B.
C.
D.
FGH
GHF
HFG
A.
B.
C.
D.
30
90
120
150
4. In the figure below, which
two angles must have equal
values?
No angle in triangle FGH
is equal to ABC .
a
f
e
2. Two parallelograms must be
similar if they are both
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l2
rectangles.
trapezoids.
squares.
rhombuses.
ACES Mathematics: Geometry Workbook
J.
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d
b
c
a and b
a and c
a and d
a and f
12
Lesson 13: Trigonometry I
Directions: Read each question carefully and then choose the best answer.
Hint: The sine ratio of an acute angle in a right triangle equals the length of the side
opposite the angle divided by the length of the hypotenuse.
In the right triangle below the
sine ratio of angle x is 0.5.
Refer to the triangle to answer
questions 1 and 2.
3. The figure pictured below is
a right triangle. Which is the
best approximation of the sine
ratio of angle a?
1. If the length of the hypotenuse is 10, what is the length of
the side opposite angle x?
aº
13
12
xº
A.
B.
C.
D.
2.5
5
7.5
10
2. If the length of the side
3
opposite angle x is 7 , what is
4
the length of the hypotenuse of
the triangle?
J.
3
K.
10
L.
15
M.
22
7
8
1
2
ACES Mathematics: Geometry Workbook
5
A.
B.
C.
D.
0.38
0.92
2.4
2.6
4. A right triangle has sides that
are 3, 4, and 5 inches long.
Which could be the sine ratio of
one of the acute angles of the
triangle?
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M.
0.25
0.4
0.6
0.95
13
Lesson 14: Trigonometry II
Directions: Read each question carefully and then choose the best answer.
1. In right triangle ABC
below, tan   0.65 and BC = 20.
What is the length of AB?
Use the figure below to answer
questions 3 and 4.
In the figure below, EFG is a
right triangle with length EF =
24 and length FG = 10.
A
E

B
C
A.
B.
C.
D.
13
12
10
8

2. In right triangle ABC below,
cos 0.80 and BC has a length
of 8. What is the length of AC?
F
G
3. Which of the following is the
closest approximation of cos?
A
A.
B.
C.
D.
0.92
0.5
0.42
0.38

B
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C
8
9
10
16
ACES Mathematics: Geometry Workbook
4. tan =
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0.42
0.92
1.1
2.4
14
Lesson 15: Trigonometry III
Directions: Read each question carefully and then choose the best answer.
1. If ABC is a right triangle with
sides AB = 3, BC = 4, and AC =
5, then sin =
3. A wire is attached to the
ground and to the top of a
telephone pole, as shown in the
diagram below.
A
pole

B
A.
B.
C.
D.
C
0.4
0.6
0.75
0.8
2. In an isosceles right triangle,
what is the approximate cosine
ratio of either acute interior
angle?
(Hint: 2  1.4 )
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wire
0.7
0.9
1
1.4
ACES Mathematics: Geometry Workbook

If the pole is 18 feet tall and
tan2.75, what is the best
approximation of the distance
from the base of the pole to the
place at which the wire meets
the ground?
A.
B.
C.
D.
4.3 feet
6.5 feet
9 feet
49.5 feet
15