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VIRGINIA STANDARDS OF LEARNING
Spring 2005 Released Test
END OF COURSE
GEOMETRY
CORE 1
Property of the Virginia Department of Education
䉷 2006 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120.
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 retrieval system,
without written permission from the copyright owner. Commonwealth of Virginia public school educators may
reproduce any portion of these released tests for noncommercial educational purposes without requesting permission.
All others should direct their written requests to the Virginia Department of Education, Division of Assessment and
Reporting at the above address or by e-mail to [email protected].
2006_GeoFormulaSht1
12/2/05
10:07 AM
Page 1
Geometry Formula Sheet
Geometric Formulas
b1
h
h
h
1
2
bh
1
2
A=
l
B
b2
b
A=
h
V = Bh
L.A. = hp
S.A.= L.A. + 2B
h(b1 + b2 )
V = 13 Bh
L.A.= 12 lp
S.A.= L.A. + B
r
w
r
r
h
l
4
3
A = lw
p = 2(l + w)
b
l
h
h
h
A = bh
l
w
V = lwh
S.A.= 2lw + 2lh + 2wh
1
3
Meaning
angle A
m
measure of angle A
Example
AB
line segment AB
AB CD
AB
measure of
line segment AB
AB CD
AB
line AB
A
ABC
triangle ABC
A
ABCD
rectangle ABCD
ABCD
parallelogram ABCD
Meaning
vector AB
right angle
AB
Copyright © 2006 by the Commonwealth of Virginia Department of Education
c2
=
a2
+ b2
Abbreviations
Geometric Symbols
Example
A
b
r
b
A
c
a
Line AB is parallel to
line CD.
Line AB is perpendicular
to line CD.
B Angle A is congruent to
angle B.
B Triangle A is similar to
triangle B.
Similarly marked
segments are congruent.
Similarly marked angles
are congruent.
Volume
Lateral Area
Total Surface
Area
Area of Base
V
L.A.
S.A.
B
Pi
22
7
2006_GeoFormulaSht1
12/2/05
10:07 AM
Page 2
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Geometry
2
DIRECTIONS
Read and solve each question. Then mark the
space on the answer sheet for the best answer.
The figure shows line l intersecting
lines r and s.
2051843
GY030622
墍
l
SAMPLE
r
A
2
D
E
B
In the figure, ∠1 and ∠2 are —
C
alternate interior angles
G alternate exterior angles
H corresponding angles 墍
J consecutive interior angles
F
If ⌬ABC is similar to ⌬ADE, then
AB : AD ⴔ ? : AE. Which replaces the
“?” to make the statement true?
AC 墍
B AE
C DE
D BC
A
1
The measures of some angles are given
in the figure.
2051787
GY030501
墌
80°
C
65°
30°
ArtCodes
x°
85°
GY030501.AR1
C
1
What is the value of x?
65
B 70 墍
C 80
D 85
A
2006 Commonwealth of Virginia Department of Education
2
ArtCodes
s
GY030622.AR1
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3
2051827
GY030580
墌
4
The Department of Transportation
wants to extend the intersecting road
across the highway, as indicated by the
dotted line.
The polygon shown is convex.
G
C
L
2051850
F
GY030632
墍
C
A
E
ArtCodes
GY030632.AR1
intersecting
road
ArtCodes
GY030580.AR1
D
B
55°
x
C
highway
The sum of its interior angle measures
is —
new construction
900⬚ 墍
G 1,260⬚
H 1,620⬚
J 2,520⬚
F
What should x be to ensure that the
intersecting road and the new
construction form a straight line?
35⬚
B 55⬚ 墍
C 105⬚
D 125⬚
A
5
A
l
2184036
GY040727
墍
C
B C
m
ArtCodes
GY040727.AR1
Which statement would be sufficient to
prove that line l is parallel to line m?
AC
B AB
C AC
D AB
A
2006 Commonwealth of Virginia Department of Education
3
⊥
⊥
⊥
⊥
m
l墍
l
AC
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6
7
In this diagram, line d cuts three lines
to form the angles shown.
Quadrilateral QRST is placed on a
coordinate grid as shown.
2051934
2051896
GY040609
GY040412
墌
C
L
墍
y
105
C
85
95
d
ArtCodes
ArtCodes
GY040609.AR1
GY040412.AR1
T (4, 6)
S (?, ?)
a
b
c
Which two lines are parallel?
Q (0, 0)
a and b
G a and c
H b and c 墍
J No lines are parallel.
x
R (8, 0)
F
What coordinates for S make QRST a
parallelogram?
(8, 6)
B (8, 10)
C (12, 6) 墍
D (12, 10)
A
8
l
!
"
$
%
#
&
m
GY040713
墍
Which condition will guarantee that
line l is parallel to line m?
∠1
G ∠1
H ∠6
J ∠3
F
2006 Commonwealth of Virginia Department of Education
4
≅
≅
≅
≅
∠3
∠6
∠5
∠5 墍
2183905
C
ArtCodes
GY040713.AR1
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9
11
A
2052484
2052497
GY110305
GY110512
墌
墍
C
L
C
ArtCodes
ArtCodes
GY110305.AR1
GY110512.AR1
The drawing shows a compass and
straightedge construction of —
W X Y Z
a perpendicular to a given line from a
point not on the line
B a perpendicular to a given line at a
point on the line
C the bisector of a given angle 墍
D an angle congruent to a given angle
A
10
To which point should a line segment
from A be drawn so that the resulting
figure is a rectangle?
W
B X 墍
C Y
D Z
A
Y
2052517
W
GY110606
墌
Z
12
C
L
⌬XYZ is similar to ⌬STR. XY ⴔ 6 and
ST ⴔ 12. If the perimeter of ⌬STR is 38,
then what is the perimeter of ⌬XYZ?
2051988
X
ArtCodes
19 墍
G 38
H 52
J 76
F
GY110606.AR1
l
T
Which point would be on a line
perpendicular to l through T?
W
G X
H Y 墍
J Z
F
2006 Commonwealth of Virginia Department of Education
5
GY05A613
墍
C
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13
15
Let p represent
公11 ⴔ z ,
3070497
2051589
If
B If
C If
D If
A
GY01B804
墌
Which of the following statements
represents a valid argument?
and let q represent
C
z is a rational number.
a
a
a
a
⬎
⬎
⬍
⬎
b
b
b
b
and
and
and
and
a
b
a
a
⬎
⬎
⬍
⬎
c,
c,
c,
c,
then
then
then
then
b ⬎ c.
a ⬎ c. 墍
c ⬍ b.
a ⬎ b ⫹ c.
GY01D407
墍
C
Which is a representation of the
statement below?
If 公11 ⴔ z, then z is not a rational
number.
16
⬃p → ⬃q
B p → q
C p → ⬃q 墍
D ⬃q → ⬃p
A
Given: ∠AXY ≅ ∠ABC
∠AYX ≅ ∠ACB
2051954
GY05A502
墍
A
C
ArtCodes
GY05A502.AR1
X
14
Y
Isosceles
Triangles
2051572
GY01C501
墌
Equilateral
Triangles
C
B
ArtCodes
Which is a true proportion?
GY01C501.AR1
According to the Venn diagram, which
statement is true?
All isosceles triangles are also
equilateral triangles.
G All equilateral triangles are also
isosceles triangles. 墍
H Some equilateral triangles are also
isosceles triangles.
J No isosceles triangles are equilateral
triangles.
F
2006 Commonwealth of Virginia Department of Education
6
F
AY
XY
AX
⫽
⫽
墍
AB
AC
BC
G
AY
XY
AX
⫽
⫽
XB
YC
BC
H
YC
BC
XB
⫽
⫽
AX
AY
XY
J
AC
XY
AX
⫽
⫽
AB
AY
BC
C
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17
2051960
19
Given: AD and BC intersect at X
AX ⴔ XB
CX ⴔ XD
X
2052067
GY05A508
墌
A
C
墍
17
15
B
GY060608
C
L
ArtCodes
X
16
Y
ArtCodes
Z
GY060608.AR1
GY05A508.AR1
C
D
In the drawing of triangle XYZ, which
angle has the least measure?
Which congruency statement is true?
All angles have the same measure.
B ∠XYZ
C ∠ZXY
D ∠XZY 墍
A
∠ACX
B ∠ACX
C ∠ACX
D ∠ACX
A
≅
≅
≅
≅
∠BXD
∠DXB
∠BDX 墍
∠DBX
20
18
2184019
Which list could not be the measures of
lengths of the three sides of a given
triangle?
C
AC,
G BA,
H BA,
J AC,
F
5 cm, 12 cm, 15 cm
G 2 ft, 6 ft, 5 ft
H 11 mi, 4 mi, 12 mi
J 12 yd, 35 yd, 20 yd 墍
F
2006 Commonwealth of Virginia Department of Education
2052048
GY060507
GY060701
墌
If m∠A ⴔ 65ⴗ, m∠B ⴔ 15ⴗ, m∠C ⴔ 100ⴗ,
which lists the sides of the triangle in
order from shortest to longest?
7
AB,
BC,
AC,
BC,
BC
AC
BC
BA 墍
墍
C
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21
2052147
GY070581
墌
23
A windlass is used to pull a boat to the
dock. The rope is attached to the boat
at a point 7 feet below the level of the
windlass.
X
2052155
45
GY070608
墍
C
C
L
ArtCodes
Y
15
Z
GY070608.AR1
ArtCodes
For the triangle represented by the
above drawing, what is the length of
XZ?
GY070581.AR1
25 ft
7 ft
7.5公2
B 7.5公3
C 15公2 墍
D 15公3
A
x ft
What is the distance from the boat to
the dock when the rope is 25 feet?
25 ft
B 24 ft 墍
C 18 ft
D 7 ft
A
24
B
C
E
2184020
GY08A709
A
22
In rectangle ABCD, which of the
following pairs of segments are not
necessarily congruent?
The parallelogram has the
measurements shown.
2052112
GY070407
墌
BD and AC
G AB and CD
H BC and DC 墍
J BE and CE
F
15
C
10
ArtCodes
h
GY070407.AR1
63°
Which is closest to the length of the
altitude, h?
19.63
G 8.91 墍
H 8.67
J 6.81
F
2006 Commonwealth of Virginia Department of Education
D
8
墍
C
ArtCodes
GY08A709.AR1
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25
2052259
GY08C516
墌
C
26
The town plaza in a certain town is a
parallelogram. The town’s planning
committee has decided to build a
fountain at the center of the plaza.
This sketch shows the corner points
when placed on a coordinate grid.
Quadrilateral ABCD is a parallelogram.
2052217
A
B
GY08A610
墍
C
L
ArtCodes
GY08A610.AR1
D
C
A (0, 4)
ArtCodes
Which of the following must be true?
GY08C516.AR1
B (6, 1)
D(
–2,
AB ≅ AD
G AC ≅ BD
H ∠A ≅ ∠D
J ∠B ≅ ∠D 墍
F
0)
C (4, –3)
27
Which coordinates show where the
fountain will be located?
ABCD is a rhombus.
2052175
B
(2, 0.5) 墍
B (0.5, 2)
C (3, 1.5)
D (1.5, 1)
C
A
墍
C
ArtCodes
A
GY08A207.AR1
40°
D
What is the measure of ∠CBD?
50⬚
B 60⬚
C 70⬚ 墍
D 75⬚
A
2006 Commonwealth of Virginia Department of Education
GY08A207
9
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28
2052316
If each interior angle of a regular
polygon measures 120ⴗ, how many
sides does the polygon have?
31
TV is a diameter of circle Z.
墌
C
2184001
T
GY090412
14
G 12
H 8
J 6 墍
GY100702
墍
F
x
8
S
C
U
ArtCodes
Z
GY100702.AR1
10
V
29
2052330
Which angle measure below is not a
possible measure of an exterior angle
of a regular polygon?
What is the value of x?
4
B 6
C 8 墍
D 10
A
GY090512
墌
C
L
36⬚
B 40⬚
C 45⬚
D 54⬚ 墍
A
32
30
C
B
2052386
A
2052357
GY100210
A
70°
GY090627
墌
O
B
P
墍
C
C
ArtCodes
D
ArtCodes
GY100210.AR1
C
GY090627.AR1
If AP ⴔ 8 and PC ⴔ 4, what is the
measure of AB, the diameter of this
circle?
In the figure, what is the measure of
∠C?
70⬚ 墍
G 90⬚
H 100⬚
J 110⬚
2
G 4
H 6 墍
J 8
F
2006 Commonwealth of Virginia Department of Education
F
10
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33
34
TW is a diameter of circle X, and TW is
parallel to UV.
This is a scale drawing of a tent where
1 centimeter represents 0.5 meter.
2052449
2052544
GY100610
GY120302
墌
T 25
C
L
墍
U
1 cm 0.5 m
ArtCodes
C
ArtCodes
GY100610.AR1
GY120302.AR1
X
W
V
៣
៣
If the measure of TU is 25ⴗ, what is the
degree measure of UV?
115⬚
B 130⬚ 墍
C 155⬚
D 210⬚
A
What is the height of the tent at its
highest point?
10 m
G 5 m
H 3 m
J 2.5 m 墍
F
2006 Commonwealth of Virginia Department of Education
11
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35
37
2052533
GY120202
墌
A spherical paintball measures
1.5 centimeters in diameter.
Approximately how much paint is in
it?
3
1.77 cm 墍
3
B 7.07 cm
3
C 9.42 cm
3
D 14.13 cm
C
L
A
ArtCodes
GY120202.AR1
Which represents a two-dimensional
view from directly above the figure?
A
2052641
GY130638
墍
C
38
ArtCodes
GY120202.AR2
GY120202.AR3
GY120202.AR4
GY120202.AR5
B
14
墍
16
15
2052713
20
C
Which proportion can be used to find
the value of PR if ⌬XMQ is similar to
⌬PRS?
D
36
2052576
GY130105
墌
C
To the nearest gallon, what is the
volume of a cylindrical water heater
1.4 feet in diameter and 4 feet tall?
(1 cubic foot ⴔ 7.48 gallons)
34 gal
G 46 gal 墍
H 59 gal
J 132 gal
F
14
20
⫽
墍
15
PR
G
7
10
⫽
5
PR
H
15
14
⫽
20
PR
J
14
15
⫽
20
PR
F
2006 Commonwealth of Virginia Department of Education
12
GY14AR26
墍
C
L
ArtCodes
GY14AR26.AR1
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39
2052724
GY14AR40
墌
When standing upright, Gary knows
his eyes are 6 feet above ground level.
To determine the depth of a well, he
stands in the position shown.
40
(3, 8)
9
2051604
8
7
GY02A102
墍
6
5
C
C
L
4
( 7, 2)
3
ArtCodes
2
GY02A102.AR1
1
9
6 ft
8
7
6
5
4
3
2
1 O
1
1
2
3
4
5
6
7
8
9
2
3
ArtCodes
4
6 ft
GY14AR40.AR1
5
2 ft
6
7
8
9
The coordinates of the midpoint of AB
are —
(5, 3)
G (⫺5, 3)
H (2, 5)
J (⫺2, 5) 墍
F
Using the given measures, how deep is
the well?
12
B 14
C 16
D 18
A
ft
ft
ft
ft 墍
2006 Commonwealth of Virginia Department of Education
13
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41
y
42
Parallelogram ABCD is placed on a
coordinate grid as shown.
2183883
A
GY02A711
B
A'
2051719
B'
GY02C412
y
墌
墍
B
C
5
C
ArtCodes
4
GY02C412.AR1
ArtCodes
GY02A711.AR1
A
3
C
2
C'
x
1
- 5 - 4 - 3 - 2 -1
D
O
-1
1
2
3C4
5
x
-2
-3
-4
-5
Triangle AⴕBⴕCⴕ is —
a translation of triangle ABC across the
y-axis 墍
G a 90⬚ clockwise rotation of triangle ABC
about the origin
H a reflection of triangle ABC across the
y-axis
J a reflection of triangle ABC across the
x-axis
F
What is the approximate length of
diagonal AC?
3.0 units
B 5.4 units 墍
C 9.0 units
D 10.6 units
A
2006 Commonwealth of Virginia Department of Education
14
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43
How many different lines of symmetry
does a square have?
44
y
2311358
GY02B701
墌
C
1
B 2
C 3
D 4 墍
A
5
2051664
4
GY02A620
墍
3
C
L
2
ArtCodes
1
–5 –4 –3 –2 –1 0
–1
–2
GY02A620.AR1
1
2
3
4
5
x
–3
–4
–5
Which is most likely the slope of the
line graphed?
F
G
H
J
2006 Commonwealth of Virginia Department of Education
15
⫺4
⫺3
2
⫺2
3
4
墍
SESSION: 34 PAGE: 16 1/13/06 6:45 LOGIN IS-garyo PATH: @sunultra1/raid/CLS_tpc/GRP_va_sprg06/JOB_06-ribsg11/DIV_g11geom-1
45
l
2051684
GY02B510
墌
C
A
B
ArtCodes
GY02B510.AR1
P
F
m
C
E
D
Hexagon ABCDEF is apparently
symmetric with respect to —
point P only
B line m only 墍
C line l only
D both lines l and m only
A
2006 Commonwealth of Virginia Department of Education
16
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Answer Key
Test
Sequence
Number
Correct
Answer
Reporting
Category
Reporting Category Description
1
B
001
Lines and Angles
2
H
001
Lines and Angles
3
B
001
Lines and Angles
4
F
001
Lines and Angles
5
B
001
Lines and Angles
6
H
001
Lines and Angles
7
C
001
Lines and Angles
8
J
001
Lines and Angles
9
C
001
Lines and Angles
10
H
001
Lines and Angles
11
B
001
Lines and Angles
12
F
002
Triangles and Logic
13
C
002
Triangles and Logic
14
G
002
Triangles and Logic
15
B
002
Triangles and Logic
16
F
002
Triangles and Logic
17
C
002
Triangles and Logic
18
J
002
Triangles and Logic
19
D
002
Triangles and Logic
20
J
002
Triangles and Logic
21
B
002
Triangles and Logic
22
G
002
Triangles and Logic
23
C
002
Triangles and Logic
24
H
003
Polygons and Circles
25
A
003
Polygons and Circles
26
J
003
Polygons and Circles
27
C
003
Polygons and Circles
28
J
003
Polygons and Circles
29
D
003
Polygons and Circles
30
F
003
Polygons and Circles
31
C
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
F
004
Three-Dimensional Figures
39
D
004
Three-Dimensional Figures
40
J
005
Coordinate Relations and Transformations
41
B
005
Coordinate Relations and Transformations
42
F
005
Coordinate Relations and Transformations
43
D
005
Coordinate Relations and Transformations
44
H
005
Coordinate Relations and Transformations
45
B
005
Coordinate Relations and Transformations