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VIRGINIA
STANDARDS OF LEARNING ASSESSMENTS
Spring 2001 Released Test
END OF COURSE
GEOMETRY
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Property of the Virginia Department of Education
䉷 2001 by the Commonwealth of Virginia Department of Education, James Monroe
Building, 101 N. 14th Street, Richmond, Virginia, 23219. All rights reserved. Except
as permitted by law, this material may not be reproduced or used in any form or by
any means, electronic or mechanical, including photocopying or recording, or by any
information storage or retrieval system, without written permission from the
copyright owner. Commonwealth of Virginia public school educators may photocopy or
print any portion of these Released Tests for educational purposes without requesting
permission. All others should direct their requests to the Commonwealth of Virginia
Department of Education at (804) 225-2102, Division of Assessment and Reporting.
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Geometry
2
DIRECTIONS
Read and solve each question. Then mark the
space on the answer sheet for the best answer.
A ladder is leaning against a house at
an angle of 38ⴗ as shown in the
diagram.
GY030205
墍
C
SAMPLE
GY05A201
A
ArtCodes
墌
D
GY030205.AR1
38°
E
House
GY05A201.AR1
ArtCodes
C
B
C
If ⌬ABC is similar to ⌬ADE, then
AB : AD ⴔ ? : AE. Which replaces the
“?” to make the statement true?
x
AC 墍
B AE
C DE
D BC
A
What is the measure of the angle, x,
between the ladder and the ground?
38⬚
G 42⬚
H 52⬚ 墍
J 142⬚
F
1
GY030105
墌
Ladder
1
C
a
ArtCodes
GY030105.AR1
40°
b
If line a is parallel to line b, what is
∠1?
m∠
40⬚ 墍
B 50⬚
C 90⬚
D 140⬚
A
3
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3
→
5
Lines AB and CD intersect at P. PR
←→
B
is perpendicular to AB , and
GY030411
墌
m ∠APD ⴔ 170ⴗ.
GY030307
墍
F
C
C
L
ArtCodes
R
GY030307.AR1
C
D
ArtCodes
A
GY030411.AR1
P
C
B
E
A
What is the measure ∠DPB?
D
10⬚ 墍
B 20⬚
C 30⬚
D 40⬚
A
Sides BC and AC of ⌬ABC are extended
to form 2 sides of parallelogram CDEF.
∠CAB and ∠CBA each measure 36ⴗ.
What is the measure of ∠CFE?
36⬚
54⬚
C 72⬚ 墍
D 108⬚
A
B
4
1
mirror
2 3
GY030209
墌
C
4 5
ArtCodes
mirror
6
6
C
F
D
GY030209.AR1
GY040102
This diagram shows how a periscope
works. If the two mirrors are parallel
and ∠1 ≅ ∠3, what is m∠6 when
m∠2 ⴔ 90ⴗ?
A
60°
40°
B
60°
45°
E
墍
G
C
ArtCodes
GY040102.AR1
Using the information on the diagram,
which is true?
30⬚
G 45⬚ 墍
H 50⬚
J 60⬚
F
4
F
BD 储 EF
G
BD 储 DE
H
CB 储 BD
J
CB 储 DE 墍
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7
9
1
a
GY040402
墌
2
3 4
GY110206
墍
5 6
7 8
b
C
Which drawing shows the arcs for a
construction of a perpendicular to a
line from a point not on the line?
C
A
ArtCodes
GY040402.AR1
ArtCodes
GY110206.AR1
GY110206.AR2
GY110206.AR3
GY110206.AR4
Line a is parallel to line b if —
m∠4
B m∠3
C m∠4
D m∠3
A
⫽
⫽
⫽
⫽
m∠2
m∠5
m∠5 墍
m∠2
B
A
8
C
GY030305
墌
C
C
ArtCodes
B
GY030305.AR1
Triangle ABC is a right triangle with
the right angle at C. Which are
possible measures for angle A and
angle B?
48⬚
G 38⬚
H 52⬚
J 52⬚
F
and
and
and
and
D
50⬚
32⬚
38⬚ 墍
128⬚
5
墍
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10
12
Use your compass and straightedge to
construct a line that is perpendicular
GY110214
墌
←→
to KL and passes through point K.
Which conclusion logically follows the
true statements?
“If negotiations fail, the baseball strike
will not end.”
C
L
GY01D101
墍
C
“If the baseball strike does not end, the
World Series will not be played.”
L
X
ArtCodes
If the baseball strike ends, the World
Series will be played.
G If negotiations do not fail, the baseball
strike will not end.
H If negotiations fail, the World Series will
not be played. 墍
J If negotiations fail, the World Series will
be played.
F
W
GY110214.AR1
Y
Z
K
Which point lies on this perpendicular?
W
G X
H Y 墍
J Z
F
13
Let a represent “x is an odd number.”
Let b represent “x is a multiple of 3.”
When x is 7, which of the following is
true?
a∧b
B a ∧ ⬃ b 墍
C ⬃ a ∧ b
D ⬃ a ∧ ⬃ b
A
11
Use your compass and straightedge to
construct the bisector of ∠GHI.
GY110215
墌
W
C
X
Y
G
ArtCodes
GY110215.AR1
Z
I
H
Which point lies on this bisector?
W
B X 墍
C Y
D Z
A
6
GY01B301
墍
C
L
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14
A
15
B
8
GY05A308
A
B
5
墌
E
C
L
?
E
D
GY05A308.AR1
墍
C
12
D
ArtCodes
GY05B304
C
C
ArtCodes
GY05B304.AR1
Given: AC ≅ BD
AD ≅ BC
In the figure, AE ⴔ 8, CE ⴔ 12, and
BE ⴔ 5. What value for the measure of
DE would make ⌬ABE similar to
⌬CDE?
Which could be used to prove
⌬ DCA ≅ ⌬CDB?
3.3
G 7.5 墍
H 8
J 15
F
7
A
(SSS) If 3 sides of one triangle are
congruent to 3 sides of another triangle,
then the triangles are congruent. 墍
B
(SAS) If 2 sides and the angle between
them in one triangle are congruent to 2
sides and the angle between them in
another triangle, then the triangles are
congruent.
C
(ASA) If 2 angles and the side between
them of one triangle are congruent to 2
angles and the side between them of
another triangle, then the triangles are
congruent.
D
(AAS) If 2 angles and a side not
between them are congruent to 2 angles
and a side not between them of another
triangle, then the triangles are
congruent.
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16
GY060401
墌
17
On the shores of a river, surveyors
marked locations, A, B, and C. The
measure of ∠ACB ⴔ 70ⴗ, and the
measure of ∠ABC ⴔ 65ⴗ.
Triangles ABC and EFG are similar
with measurements as shown.
GY05A405
墍
G
C
C
B
C
ArtCodes
7
ArtCodes
GY060401.AR1
A 5
A
A
G B
H B
J A
to
to
to
to
B,
C,
C,
C,
B
E
10
F
C
What is the ratio
Which lists the distances between
these locations in order, least to
greatest?
F
GY05A405.AR1
9
B
A
A
A
to
to
to
to
C,
B,
C,
B,
A
A
A
B
to
to
to
to
C
C
B墍
C
18
A
1
墍
2
B
5
7
C
7
10
D
7
9
Which of the following could be the
lengths of the sides of ⌬ ABC?
AB
G AB
H AB
J AB
F
8
AC
?
EG
⫽
⫽
⫽
⫽
12, BC ⫽ 15, AC ⫽ 2
9, BC ⫽ 15, CA ⫽ 4
150, BC ⫽ 100, CA ⫽ 50
10, BC ⫽ 8, AC ⫽ 12 墍
GY060110
墍
C
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19
20
Three lookout towers are located at
points A, B, and C on the section of a
national forest shown in the drawing.
GY060304
墌
C
20 ft
C
5,385m
ArtCodes
60°
GY060304.AR1
B
4,123m
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;;;;
GY070305
墍
C
L
ArtCodes
GY070305.ART
72m
4,4
A 20-foot ladder leaning against a
building makes an angle of 60ⴗ with the
ground. How far from the base of the
building is the foot of the ladder?
A
Which of the following statements is
true concerning ⌬ABC formed by the
towers?
5 ft
G 8.2 ft
H 10 ft 墍
J 17.3 ft
F
m∠A is greatest. 墍
B m∠C is greatest.
C m∠A is least.
D m∠C is least.
A
21
A
GY070410
墍
C
B
2
D
8
C
In the figure, ⌬ABC is a right triangle.
AD is perpendicular to BC, and the
measure of BD ⴔ 2 meters and DC ⴔ 8
meters. What is the measure of AC?
2.8 m
B 4.5 m
C 8.9 m 墍
D 10.0 m
A
9
ArtCodes
GY070410.AR1
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22
y
24
P
A (2, 3)
GY070110
墌
C
B (?, ?)
6 mi
A
34 mi
D (0, 0)
GY070110.AR1
An airplane is 34 ground miles from
the end of the runway (GA) and 6 miles
high (PG) when it begins its approach
to the airport. To the nearest mile,
what is the distance (PA) from the
airplane to the end of the runway?
41
G 39
H 37
J 35
F
(3,
G (5,
H (7,
J (7,
F
mi
mi
mi
mi 墍
23
R
GY070121
墌
C
O
T
In circle O, ∠RST formed by chord RS
and diameter ST has a measure of 30ⴗ.
If the diameter is 12 centimeters, what
is the length of chord SR?
A
12公3 cm
B
12公2 cm
C
6公3 cm墍
D
6公2 cm
ArtCodes
GY08B301.AR1
7)
5)
8)
3) 墍
A rhombus
B A rectangle
C A parallelogram
D A trapezoid 墍
S
x
Which of the following quadrilaterals
could have diagonals that are
congruent but do not bisect each
other?
A
GY070121.AR1
C (5, 0)
If ABCD is a parallelogram, what are
the coordinates of B?
25
ArtCodes
墍
C
G
ArtCodes
GY08B301
10
GY08A301
墍
C
L
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26
GY08C407
墌
27
Three vertices of a square have
coordinates (5, 1), (2, ⴑ2), and (ⴑ1, 1).
You may want to plot the points on this
grid.
C
The figure has angle measures as
shown.
GY090410
墍
D
C
y
C 5x + 10
ArtCodes
GY090410.AR1
ArtCodes
A
GY08C407.AR1
3x
3x
B
What is the measure of ∠BCD?
x
120⬚
B 80⬚
C 60⬚ 墍
D 30⬚
A
28
What are the coordinates of the fourth
vertex?
x°
(⫺2, 2)
G (2, ⫺2)
H (2, 4) 墍
J (4, 2)
GY090201
F
墍
C
ArtCodes
GY090201.AR1
A floor tile is designed with a
regular pentagon in the center of the
tile with its sides extended. What is
the value of x?
72⬚ 墍
G 90⬚
H 110⬚
J 120⬚
F
11
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29
31
Each exterior angle of a certain
regular polygon measures 30ⴗ. How
many sides does the polygon have?
D
3
GY090311
墌
C
L
A
6
B 9
C 10
D 12 墍
A
GY100314
墍
2
C
L
R
5
B
C
30
Chords AB and CD intersect at R.
Using the values shown in the
diagram, what is the measure of RB?
GY100214
墌
C
L
ArtCodes
GY100214.AR1
6
B 7.5 墍
C 8
D 9.5
A
R
O
P
45°
S
A circle for a game spinner is divided
into 3 regions as shown. RP is a
diameter. What is the area of the
shaded sector ROS if RP ⴔ 8?
1.5 ␲
G 6 ␲ 墍
H 24 ␲
J 72 ␲
F
12
ArtCodes
GY100314.AR1
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32
33
The logo of an airline is a circle
inscribed in a triangle.
140°
A
GY100113
墌
B
GY100311
墍
C
C
C
C
180°
ArtCodes
GY100113.AR1
When inscribed in a certain circle,
⌬ABC intercepts arcs as shown in the
diagram. What is the measure of
∠ BAC?
90⬚
B 70⬚
C 40⬚
D 20⬚ 墍
A
E
F
A
D
B
If AF ⴔ 3 and AB ⴔ 11, then BD ⴔ
?
8墍
G 10
H 11
J 12
F
13
ArtCodes
GY100311.AR1
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34
This is one view of a 3-dimensional
object.
35
GY120214
GY120108
墌
墍
C
L
C
ArtCodes
GY120108.AR1
ArtCodes
GY120214.AR1
Which is a different view of the same
object?
ArtCodes
SCALE
1 cm Represents 13 m
This is a scale drawing of a building.
What is the actual height of the
building?
F
58.5 m 墍
B 71.5 m
C 78 m
D 84.5 m
A
GY120214.AR2
GY120214.AR3
GY120214.AR4
GY120214.AR5
G
36
What is the volume in cubic feet of a
refrigerator whose interior is 4.5 feet
tall, 2.5 feet wide, and 2 feet deep?
GY130106
15 cu ft
G 19 cu ft
H 22.5 cu ft 墍
J 25 cu ft
F
H
J
墍
14
墍
C
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37
38
GY130103
墌
8m
C
ArtCodes
6m
GY130103.AR1
Two vehicles, each moving from a
point in a straight line away from each
other at an angle, are 150 feet apart
after 6 seconds. Both are moving at a GY140206
墍
constant rate, vehicle A at 50 feet per C
second and vehicle B at 40 feet per
L
second.
le A
10m
ic
eh
V
150 ft
ArtCodes
GY140206.AR1
Vehicle B
How far apart are they after
15 seconds?
Rounded to the nearest hundred cubic
meters, what is the total capacity (cone
and cylinder) of the storage container?
150
G 375
H 600
J 750
F
1,400 墍
B 2,000
C 5,700
D 8,100
A
15
ft
ft 墍
ft
ft
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39
GY140212
墌
C
In order to determine the height of a
tree, Marı́a places a mirror flat on the
ground 25 feet from the base. After
backing 3.25 feet, she can just see the
top of the tree in the mirror.
y
40
A
D
GY02B302
墍
C
L
B
ArtCodes
GY02B302.AR1
5 ft
ArtCodes
C
3.25 ft
GY140212.AR1
25 ft
Marı́a knows that her eyes are exactly
5 feet above ground level and that the
angle between her eyes, the mirror,
and the ground is the same as the
angle between the tree top, the mirror,
and the ground. Which is closest to the
height of the tree?
24
B 28
C 38
D 40
A
Quadrilateral ABCD is symmetric with
respect to the y axis. If the coordinates
of B are (2, 1), what are the
coordinates of D?
(⫺2,
G (⫺1,
H (⫺2,
J (⫺1,
F
ft
ft 4 in.
ft 6 in. 墍
ft
41
⫺1)
⫺2)
1) 墍
2)
If RS ⴔ (3, ⴑ2) and TV ⴔ (ⴑ1, ⴑ4), which
column matrix shows the resultant
RS ⴐ TV ?
A
冋册
冋册
冋册
冋册
2
墍
⫺6
4
B
C
2
⫺4
⫺2
⫺6
D
16
2
GY15A107
墍
C
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y
42
44
B
BC ⴔ (2, 4)
ⴑ
AB ⴔ (4, ⴑ3)
CD ⴔ ( 1, 1)
GY02C413
墌
C
Which matrix gives the resultant AD of
GY02C413.AR1
A
C
the vector sum AB ⴐ BC ⴐ CD ?
ArtCodes
冋册
冋册
冋册
冋册
5
F
x
A'
G
墍
2
GY15A208
墍
C
L
3
⫺2
5
H
B'
⫺5
J
Triangle AⴕBⴕC is —
a translation of triangle ABC across the
y-axis
G a 180⬚ rotation of triangle ABC about
the origin 墍
H a reflection of triangle ABC across the
y-axis only
J a reflection of triangle ABC across the
x-axis only
8
4
F
45
Joan drives 3 miles north, turns east
for 2 miles, then north again for 4
miles, and finally 5 miles east. Which
vector could be used to describe the
resultant of her drive?
(5,
B (5,
C (7,
D (7,
A
43
A circle whose center is at (1, ⴑ3)
passes through (7, 5). What is the
length of the radius of the circle?
GY02A204
墌
C
10 墍
公40
C 公68
D 14
A
B
17
9)
10)
7) 墍
10)
GY15B203
墍
C
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Answer Key
Test
Sequence
Correct
Answer
Reporting
Category
Reporting Category Description
1
A
001
Lines and Angles
2
H
001
Lines and Angles
3
A
001
Lines and Angles
4
G
001
Lines and Angles
5
C
001
Lines and Angles
6
J
001
Lines and Angles
7
C
001
Lines and Angles
8
H
001
Lines and Angles
9
D
001
Lines and Angles
10
H
001
Lines and Angles
11
B
001
Lines and Angles
12
H
002
Triangles and Logic
13
B
002
Triangles and Logic
14
G
002
Triangles and Logic
15
A
002
Triangles and Logic
16
H
002
Triangles and Logic
17
A
002
Triangles and Logic
18
J
002
Triangles and Logic
19
A
002
Triangles and Logic
20
H
002
Triangles and Logic
21
C
002
Triangles and Logic
22
J
002
Triangles and Logic
23
C
002
Triangles and Logic
24
J
003
Polygons and Circles
25
D
003
Polygons and Circles
26
H
003
Polygons and Circles
27
C
003
Polygons and Circles
28
F
003
Polygons and Circles
29
D
003
Polygons and Circles
30
G
003
Polygons and Circles
31
B
003
Polygons and Circles
32
F
003
Polygons and Circles
33
D
003
Polygons and Circles
34
J
004
Three-Dimensional Figures
35
A
004
Three-Dimensional Figures
36
H
004
Three-Dimensional Figures
37
A
004
Three-Dimensional Figures
38
G
004
Three-Dimensional Figures
39
C
004
Three-Dimensional Figures
40
H
005
Coordinate Relations, Transformations, and Vectors
41
A
005
Coordinate Relations, Transformations, and Vectors
42
G
005
Coordinate Relations, Transformations, and Vectors
43
A
005
Coordinate Relations, Transformations, and Vectors
44
F
005
Coordinate Relations, Transformations, and Vectors
45
C
005
Coordinate Relations, Transformations, and Vectors