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VIRGINIA
STANDARDS OF LEARNING ASSESSMENTS
Spring 2002 Released Test
END OF COURSE
GEOMETRY
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Property of the Virginia Department of Education
䉷 2002 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.
George used a decorative fencing to
enclose his deck.
GY030102
x
SAMPLE
墍
C
GY05A201
A
ArtCodes
130°
D
墌
E
GY030102.AR1
50°
B
GY05A201.AR1
ArtCodes
C
Using the information on the diagram
and assuming the top and bottom are
parallel, the measure of ∠x is —
C
If ⌬ABC is similar to ⌬ADE, then
AB : AD ⴔ ? : AE. Which replaces the
“?” to make the statement true?
50⬚ 墍
G 80⬚
H 100⬚
J 130⬚
F
AC 墍
B AE
C DE
D BC
A
3
Angle 1 is a complement of angle 2. If
m∠1 ⴔ (14x ⴐ 8) and m∠2 ⴔ (8x ⴑ 6),
what is the value of x and of m∠1?
GY030505
x
B x
C x
D x
A
1
3
GY030106
墌
C
L
65°
150°
ArtCodes
GY030106.AR1
∠3?
What is m∠
65⬚
B 75⬚
C 85⬚ 墍
D 90⬚
A
2002 Commonwealth of Virginia Department of Education
3
⫽
⫽
⫽
⫽
4, m∠1 ⫽ 26⬚
4, m∠1 ⫽ 64⬚ 墍
113.3, m∠1 ⫽ 121.3⬚
113.3, m∠1 ⫽ 58.7⬚
墍
C
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4
l
6
In the figure, lines l and m are cut by
the transversal t forming the angles
shown.
120°
w
GY030575
墌
80°
C
x
t
y
70°
1
ArtCodes
GY030575.AR1
3
5
8
2
ArtCodes
GY040116.AR1
100°
m
7
Line l intersects lines w, x, y, and z.
Which two lines are parallel?
Vertical angles
G Corresponding angles
H Alternate interior angles 墍
J Alternate exterior angles
F
Use this figure to answer the following.
7
A
GY040513
B
C
C
4
6
墌
墍
z
l
∠3 and ∠6 are —
5
GY040116
1
2
F
Line w and line x
G
Line w and line y
H
Line x and line z 墍
J
Line y and line z
The measure of ∠YZV is 40ⴗ and the
measure of ∠XYZ is 65ⴗ.
GY040450
墍
X
l
C
L
ArtCodes
GY040513.AR1
3
4
C
V
m
ArtCodes
GY040450.AR1
D
→
Y
→
m∠1
B m∠3
C m∠1
D m∠1
⫽
⫽
⫹
⫹
m∠2
m∠4
m∠2 ⫽ 90
m∠2 ⫽ m∠3 ⫹ m∠4 墍
2002 Commonwealth of Virginia Department of Education
Z
Which of these angles must measure
40ⴗ in order for VR to be parallel to YZ?
BA is parallel to CD if —
A
R
∠YVZ
B ∠ZVR 墍
C ∠ZYV
D ∠VRX
A
4
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8
9
Lines l and m contain the points
shown.
GY040452
墌
Use a compass, a straightedge, and the
drawing below to answer the question.
y
GY110407
墍
R
C
C
L
6
l
(–3, 3)
ArtCodes
m
GY040452.AR1
(–5, 1)
S
5
Q
4
GY110407.AR1
2
(6, 0)
1
–6 –5 –4 –3 –2 –1
ArtCodes
3
0
–1
–2
1
2
3
4
5
6
x
P
A
B
–3
–4
T
–5
–6
Which point lies on the line through P
perpendicular to AB?
Which of the following points must lie
on line m in order for lines l and m to
be parallel?
(0,
G (0,
H (1,
J (4,
F
Q墍
B R
C S
D T
A
⫺2)
⫺1)
⫺1) 墍
⫺1)
10
X
Y
GY110509
墍
C
ArtCodes
GY110509.AR1
A
B
Z
W
Which pair of points determines the
perpendicular bisector of line segment
AB?
X,W
G X,Z 墍
H Y,W
J Y,Z
F
2002 Commonwealth of Virginia Department of Education
5
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11
12
Use your compass and straightedge to
construct the bisector of this angle.
Which of the following groups of
statements represents a valid
argument?
GY110110
墌
F
C
L
ArtCodes
GY110110.AR1
G
I
再
All quadrilaterals have four sides.
Given: All squares have four sides.
GY01D409
Conclusion: All quadrilaterals are
墍
squares.
C
再
All squares have congruent sides.
Given: All rhombuses have congruent
sides.
Conclusion: All rhombuses are squares.
J
冦
All four sided figures are
quadrilaterals.
H Given:
All parallelograms have four 墍
sides.
Conclusion: All parallelograms are
quadrilaterals.
K
L
Which point lies on the bisector?
I
B J
C K 墍
D L
A
J
13
再
All rectangles have angles.
Given: All squares have angles.
Conclusion: All rectangles are squares.
Which is the contrapositive of the
statement, “If I am in Richmond, then I
GY01A404
am in Virginia”?
墍
If I am in Virginia, then I am in
Richmond.
B If I am not in Richmond, then I am not
in Virginia.
C If I am not in Virginia, then I am not in
Richmond. 墍
D If I am not in Virginia, then I am in
Richmond.
A
2002 Commonwealth of Virginia Department of Education
6
C
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14
A
15
B
Given: AE and BD bisect each other
at C.
GY05A301
墌
GY05B301
墍
D
C
L
C
A
C
E
ArtCodes
GY05A301.AR1
B
C
R
Which of the following correctly
describes the relationship between the
sides of ⌬ABC and ⌬TRC?
AC
BC
AB
⫽
⫽
TR
RC
TC
G
BC
TR
AC
⫽
⫽
AB
RC
TC
H
BC
TR
AB
⫽
⫽
AC
RC
TC
J
AC
BC
AB
⫽
⫽
墍
TR
TC
RC
2002 Commonwealth of Virginia Department of Education
GY05B301.AR1
Which could be used to prove
⌬ABC ≅ ⌬EDC?
T
F
ArtCodes
7
A
(SSS) If 3 sides of one triangle are
congruent to 3 sides of another triangle,
then the triangles are congruent.
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. 墍
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
18
A surveyor made this sketch from
measurements he made along a river.
GY05A503
墌
In the drawing, the measure of
∠C ⴔ 125ⴗ and the measure of ∠B ⴔ 35ⴗ.
GY060403
墍
B
T
C
B
ArtCodes
GY05A503.AR1
A
80 ft
120 ft
D
ArtCodes
125°
C
40 ft
C
AC
G AB
H EB
J BC 墍
60 ft 墍
G 69.3 ft
H 84.9 ft
J 120 ft
19
A
GY060575
墌
C
B
GY060575.AR1
59°
57°
AC,
B AB,
C BC,
D AB,
BC,
BC,
AC,
AC,
5 miles
B 10 miles
C 150 miles 墍
D 200 miles
AB
AC
AB
BC 墍
2002 Commonwealth of Virginia Department of Education
On a map, Tannersville, Chadwick, and
Barkersville form a triangle. Chadwick
is 70 miles from Tannersville and
GY060102
Barkersville is 90 miles from
墍
Tannersville. Which is a possible
C
distance between Chadwick and
Barkersville?
A
C
From shortest to longest, the sides of
⌬ABC are —
A
A
F
F
17
GY060403.AR1
Which is the shortest side of the
triangle?
What is the distance across the river
from point A to point T?
ArtCodes
C
L
35°
8
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20
22
5 cm
GY070308
墌
The lengths of 2 consecutive sides of
the parallelogram shown are 10 inches
and 15 inches. The 2 sides include an
GY070430
angle of 60ⴗ.
墍
C
B
C
C
L
ArtCodes
Radius
GY070308.AR1
10
30°
ArtCodes
GY070430.AR1
60°
A
The drawing shows the measurements
in a section of a circular design. How
long is the radius of the circle?
21.6 sq in.
G 129.9 sq in. 墍
H 139.4 sq in.
J 140.5 sq in.
F
10 cm 墍
G 8.7 cm
H 7 cm
J 4.3 cm
A carpenter is building a flight of
stairs as pictured in the drawing.
GY070514
墌
C
20
ArtCodes
ft
wall
GY070514.AR1
30°
floor
What is the horizontal distance from
the foot of the stairs to the wall?
14.1
B 17.3
C 20.0
D 28.3
A
ft
ft 墍
ft
ft
2002 Commonwealth of Virginia Department of Education
D
To the nearest tenth of a square inch,
what is the area of the parallelogram?
F
21
15
9
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23
24
A
25°
GY070124
B
GY08A103
墌
墍
70°
C
48 ft
D
ArtCodes
GY070124.AR1
70⬚
G 45⬚
H 35⬚
J 25⬚ 墍
F
A cable 48 feet long stretches from the
top of a pole to the ground. If the cable
forms a 40ⴗ angle with the ground,
which is closest to the height of the
pole?
sin 40ⴗ ⬇ 0.642
cos 40ⴗ ⬇ 0.766
tan 40ⴗ ⬇ 0.839
26.4
B 30.9
C 36.8
D 40.3
ft
ft 墍
ft
ft
2002 Commonwealth of Virginia Department of Education
C
In parallelogram ABCD, what is
∠BDC?
m∠
40°
A
C
35°
10
ArtCodes
GY08A103.AR1
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25
26
L
3x°
95°
M
GY08B202
墌
C
K
Three vertices of a parallelogram have
coordinates (0, 1), (3, 7), and (4, 4). You
may want to plot the points on this
GY08C409
grid.
墍
(x+25)°
ArtCodes
C
L
y
80°
N
GY08B202.AR1
Given quadrilateral KLMN, what is the
value of x?
ArtCodes
GY08C409.AR1
35
B 40 墍
C 45
D 50
A
x
What are the coordinates of the
fourth-quadrant vertex?
(⫺2, 1)
G (1, ⫺2) 墍
H (2, ⫺1)
J (3, 3)
F
27
A
B
C
F
GY090107
Q
E
墍
C
D
ArtCodes
GY090107.AR1
Figure ABCDEF is a regular hexagon.
What is the measure of ∠CDQ?
45⬚
B 60⬚ 墍
C 90⬚
D 120⬚
A
2002 Commonwealth of Virginia Department of Education
11
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28
In pentagon ABCDE, m∠E ⴔ m∠C and
m∠D ⴔ m∠B.
30
GY090508
墌
A
Triangle ABC is circumscribed
about circle O. P and Q are points
of tangency such that
BP ⴔ 3 and CQ ⴔ 5.
GY100213
墍
C
C
E
105°
B
B
ArtCodes
3
GY090508.AR1
100°
D
ArtCodes
C
GY100213.AR1
P
O
What is the measure of ∠A?
C
410⬚
G 335⬚
H 155⬚
J 130⬚ 墍
F
5
Q
A
What is the measure of BC?
3
G 4
H 5
J 8 墍
F
29
The figure has angle measures as
shown.
GY090409
墌
A
C
L
19x – 15
ArtCodes
26x + 20
GY090409.AR1
D
9x + 25
B
31
C
D
C
GY100303
墍
C
L
What is the measure of ∠ABD?
ArtCodes
150⬚ 墍
B 80⬚
C 70⬚
D 30⬚
A
A
GY100303.AR1
40°
B
∠CAB ⴔ 40ⴗ, what is m∠
∠CDB?
If m∠
20⬚
B 40⬚ 墍
C 60⬚
D 80⬚
A
2002 Commonwealth of Virginia Department of Education
12
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32
←→
AB is tangent to circle C at B, AB ⴔ 15
centimeters, and the radius of the
circle is 8 centimeters.
34
GY100511
GY120206
墌
墍
C
A
C
L
B
ArtCodes
GY120206.AR1
ArtCodes
C
GY100511.AR1
Which are the top, side, and front
views of the object shown above?
To the nearest tenth of a centimeter,
what is the length of AC?
F
7.0 cm
G 12.7 cm
H 17.0 cm 墍
J 23.0 cm
F
ArtCodes
GY120206.AR2
GY120206.AR3
GY120206.AR4
GY120206.AR5
G
H
33
This is a sketch of a stained-glass
window in the shape of a semicircle.
GY100580
墌
J
C
ArtCodes
GY100580.AR1
8 ft
Ignoring the seams, how much glass is
needed for the window?
4␲ sq ft
B 8␲ sq ft 墍
C 12␲ sq ft
D 16␲ sq ft
A
2002 Commonwealth of Virginia Department of Education
13
墍
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35
37
2.44 m
8.20 m
GY130304
GY130202
墌
墍
C
C
2.76 m
ArtCodes
ArtCodes
The water level in a rectangular prism GY130202.AR1
tank 40 centimeters by 20 centimeters
is 12 centimeters high. A rock
submerged in the tank raises the water
level 0.4 centimeters. What is the
volume of the rock?
GY130304.AR1
320 cm3 墍
3
B 960 cm
3
C 2,000 cm
3
D 9,920 cm
The cargo space of the truck is 2.44
meters wide, 2.76 meters high, and
8.20 meters long. How many cubic
meters of cargo space does the truck
have?
26.80
B 55.22 墍
C 98.75
D 110.44
A
A
38
The ratio between the volumes of two
spheres is 27 to 8. What is the ratio
between their respective radii?
GY140406
81 : 64
G 27 : 16
H 9:8
J 3:2 墍
F
36
What is the approximate volume of a
can that is 5 inches tall and has a
2.5 inch diameter?
GY130508
墌
C
19.6
G 24.5
H 39.3
J 98.1
F
cu
cu
cu
cu
in.
in. 墍
in.
in.
2002 Commonwealth of Virginia Department of Education
14
墍
C
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39
40
All the vertices of the hexagon have
integral coordinates.
GY140104
墌
GY02B401
墍
y
C
L
C
L
d
ArtCodes
GY140104.AR1
ArtCodes
GY02B401.AR1
9 ft
12 ft
52 ft
1
1
The distance across a river was
estimated by making the
measurements shown. Which is a good
estimate of the distance d?
20
B 30
C 40
D 50
A
ft
ft
ft 墍
ft
One of the lines of symmetry for the
hexagon goes through —
(⫺4, 3) and (4, 3) 墍
G (⫺2, ⫺2) and (2, 7)
H (⫺2, 7) and (2, ⫺2)
J (2, ⫺2) and (⫺2, ⫺7)
F
2002 Commonwealth of Virginia Department of Education
15
x
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y
41
43
The coordinates of the midpoint of AB
are (ⴑ2, 1), and the coordinates of A are
(2, 3). What are the coordinates of B?
GY02C411
GY02A408
墌
A
(0, 2)
B (⫺1, 2)
C (⫺3, 4)
D (⫺6, ⫺1) 墍
A
C
E
B
ArtCodes
GY02C411.AR1
D
D'
C
C'
E'
x
B'
A'
The polygon AⴕBⴕCⴕDⴕEⴕ is —
a translation of ABCDE across the
x-axis
B a 180⬚ clockwise rotation of ABCDE
about the origin
C a reflection of ABCDE across the y-axis
D a reflection of ABCDE across the x-axis 墍
A
42
If CD ⴔ (5, 3) and EF ⴔ (7, ⴑ4), which
column matrix shows the resultant
GY15A108
墌
C
CD ⴐ EF ?
F
G
H
J
冋
冋
冋
冋
册
册
册
册
12
⫺7
⫺7
12
12
墍
⫺1
⫺1
12
2002 Commonwealth of Virginia Department of Education
16
墍
C
L
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44
is a graph of PQ ⴐ CD ?
If PQ ⴔ (2, 2) and CD ⴔ (3, ⴑ2), which
45
GY15A502
墌
An airplane is headed due north at
300 nautical miles per hour (knots) as
shown in the drawing. The wind is
directly from the east at 50 knots.
y
C
GY15B401
墍
C
9
8
7
6
5
4
3
ArtCodes
GY15A502.AR1
GY15A502.AR2
GY15A502.AR3
GY15A502.AR4
2
F
1
-9
-8
-7
-6
-5
-4
-3
-2
-1 0
-1
1
2
3
4
5
6
7
8
9
x
ArtCodes
-2
-3
GY15B401.AR1
-4
-5
-6
-7
300
-8
-9
y
9
8
7
6
5
4
墍
3
G
2
1
-9
-8
-7
-6
-5
-4
-3
-2
-1 0
-1
1
2
3
4
5
6
7
8
9
x
-2
-3
Which is closest to the resultant speed
of the airplane?
-4
-5
-6
-7
-8
-9
314
B 304
C 296
D 286
A
y
9
8
7
6
5
4
H
3
2
1
-9
-8
-7
-6
-5
-4
-3
-2
-1 0
-1
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
-2
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
J
4
3
2
1
-9
-8
-7
-6
-5
-4
-3
-2
-1 0
-1
x
-2
-3
-4
-5
-6
-7
-8
-9
2002 Commonwealth of Virginia Department of Education
17
knots
knots 墍
knots
knots
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Answer Key
Test
Sequence
Correct
Answer
Reporting
Category
1
C
001
Lines and Angles
2
F
001
Lines and Angles
Reporting Category Description
3
B
001
Lines and Angles
4
H
001
Lines and Angles
5
D
001
Lines and Angles
6
H
001
Lines and Angles
7
B
001
Lines and Angles
8
H
001
Lines and Angles
9
A
001
Lines and Angles
10
G
001
Lines and Angles
11
C
001
Lines and Angles
12
H
002
Triangles and Logic
13
C
002
Triangles and Logic
14
J
002
Triangles and Logic
15
B
002
Triangles and Logic
16
F
002
Triangles and Logic
17
D
002
Triangles and Logic
18
J
002
Triangles and Logic
19
C
002
Triangles and Logic
20
F
002
Triangles and Logic
21
B
002
Triangles and Logic
22
G
002
Triangles and Logic
23
B
002
Triangles and Logic
24
J
003
Polygons and Circles
25
B
003
Polygons and Circles
26
G
003
Polygons and Circles
27
B
003
Polygons and Circles
28
J
003
Polygons and Circles
29
A
003
Polygons and Circles
30
J
003
Polygons and Circles
31
B
003
Polygons and Circles
32
H
003
Polygons and Circles
33
B
003
Polygons and Circles
34
J
004
Three-Dimensional Figures
35
B
004
Three-Dimensional Figures
36
G
004
Three-Dimensional Figures
37
A
004
Three-Dimensional Figures
38
J
004
Three-Dimensional Figures
39
C
004
Three-Dimensional Figures
40
F
005
Coordinate Relations, Transformations, and Vectors
41
D
005
Coordinate Relations, Transformations, and Vectors
42
H
005
Coordinate Relations, Transformations, and Vectors
43
D
005
Coordinate Relations, Transformations, and Vectors
44
G
005
Coordinate Relations, Transformations, and Vectors
45
B
005
Coordinate Relations, Transformations, and Vectors