Geometry EOC
SOL Simulation
Graphing Calculator Active
Chesterfield County Public Schools
Department of Mathematics
2011-2012
1
George used a decorative gate to connect the fencing around his
backyard.
B
C
A
E
120
60
F
G
Using the information on the diagram and assuming the top and
bottom are parallel, mABC is —
A
B
C
D
2
40º
60º
120º
180º
Which is the biconditional of the following statement?
If a polygon is a triangle, then it has exactly three sides.
A
A polygon is not a triangle if and only if it does not have three sides.
B
A polygon is a triangle if and only if it has exactly three sides.
C
If a polygon has exactly three sides, then it is a triangle.
D
If a polygon does not have exactly three sides, then it is not a
triangle.
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 1 of 29
2011-12
3
Given: p || q , m || n , and m1  75 .
1
q
p
2
m
n
What is m2 ?
A
B
C
D
4
15º
75º
105º _
165º
Given: angle A
What is the first step in constructing the angle bisector of angle A?
B
D
A
A
B
C
D
C
Draw AD .
Draw a line segment connecting points B and C.
From points B and C, draw equal arcs that intersect at D.
From point A, draw an arc that intersects each side of the angle.
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 2 of 29
2011-12
In the diagram, A' B' C' is a transformation of ABC , and
A" B" C" is a transformation of A' B' C' .
y
5
C
B
C’
C”
B’
B”
A’
A”
A
x
The composite transformation of ABC to ABC is an example
of a
A
B
C
D
6
reflection followed by a rotation.
reflection followed by a translation.
translation followed by a rotation.
translation followed by a reflection.
Determine which statement best represents the information in the
figure.
E
70
F
30
68
32
30
A
A
AE || CF and EB || FD
B
AD || EF and EB || FD
C
AD || EF and CF || FD
D
AE || CF and EF || AD
Geometry EOC SOL Simulation
Chesterfield County Public Schools
BC
D
Page 3 of 29
2011-12
7
Which conclusion logically follows the true statements?
 “If the football team doesn’t score, they will lose the game.”
 “If the football team loses the game, they will not play for
the championship.”
A
B
C
D
If
If
If
If
the
the
the
the
football
football
football
football
Geometry EOC SOL Simulation
Chesterfield County Public Schools
team
team
team
team
wins, they will not play for the championship.
scores, they will play for the championship.
doesn’t score, they will play for the championship.
doesn’t score, they will not play for the championship.
Page 4 of 29
2011-12
8
Given: k || p.
1
2
k
3 4
5
6
p
Which of the following is NOT a valid proof that m1  m6  180 ?
A
Statements
1. k || p
2. m1  m5
3. m5  m6  180
4. m1  m6  180
B
Statements
1. k || p
2. m1  m4
3. m4  m6  180
4. m1  m6  180
C
Statements
1. k || p
2. m1  m2  180
3. m2  m6
4. m1  m6  180
D
Reasons
1. Given
2. If two parallel lines are cut by a
transversal, corresponding angles are
congruent
3. Definition of linear pair
4. Substitution property
Reasons
1. Given
2. Definition of vertical angles.
3. If two parallel lines are cut by a
transversal, same side interior angles are
supplementary
4. Substitution property
Reasons
1. Given
2. If two parallel lines are cut by a
transversal, alternate exterior angles are
supplementary
3. If two parallel lines are cut by a
transversal, corresponding angles are
congruent
4. Substitution property
Statements
Reasons
1. Given
1. k || p
2. m1  m3  180 2. Definition of linear pair
3. corresponding
If two parallelangles
lines are
by a
3.2. If
m
3  lines
m6 are parallel,
two
are cut
congruent.
transversal,
alternate
interior
angles are
3. Vertical angles are congruent.
congruent
4. m1  m6  180 4. Substitution property
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 5 of 29
2011-12
9
Which geometric construction is shown in the diagram?
A
A
B
C
D
10
a
a
a
a
B
line segment congruent to a given line segment.
line parallel to a given line
perpendicular bisector of a segment
bisector of a given angle
Quadrilateral ABCD has vertices A (-2, 2), B (4, 5), C (3, 0) and
D (-3,-3). What are the coordinates of the midpoint of
diagonal BD ?
A
B
C
D
1

 ,1 
2

1 
 ,1 
2 
 1
1, 
 2
(1, 1)
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 6 of 29
2011-12
11 If p||q, what is the measure of ACB ?
A
 5 x  14 
19 x  28
p
C
B
A
B
C
D
12
3°
29°
151°
177°
q
t
1
x 2.
3
The equation of line m is  2 x  6 y  18 .
The equation of line k is y 
Lines k and m are –
A
B
C
D
parallel
perpendicular
the same line
intersecting but not perpendicular
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 7 of 29
2011-12
13 Given: LM and QR are parallel
Given: m  M = m  L = 50°.
M
L
R
N
P
Q
What is mQNP ?
A
B
C
D
130º
100º _
80º
50º
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 8 of 29
2011-12
14 Scott is constructing a line perpendicular to line l from point P.
Which of the following should be his first step?
A
B
_
C
D
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 9 of 29
2011-12
15
Students’ After School Activities
Sports
Clubs
Music
Based strictly on this diagram representing students
participating in after school activities, which statement
represents the shaded region?
A
B
C
D
Some students participate in sports and music, but not clubs.
Some students participate in clubs and music, but not sports.
Some students participate in sports, music, and clubs.
All students participate in sports and music.
16
If triangle XYZ is reflected across the x-axis to form triangle
X 'Y 'Z', what are the coordinates of Z' ?
A
B
C
D
(2, -3)
(2, 3)
(-2, 3)
(3, 2)
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 10 of 29
2011-12
17
Consider the following statements represented by p and q :
p: The sum of two angles is 180°.
q: The two angles are supplements.
Which of the following is a symbolic representation of the
statement
If two angles are not supplements, then the sum of
the two angles is not 180°.
A
B
C
D
q p_
p q
~q  ~ p
~p  ~ q
18
This figure has —
A
B
C
D
point symmetry only
line symmetry only_
point and line symmetry
neither point nor line symmetry
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 11 of 29
2011-12
19
QJK ~ QRS .
Which of the following statements is NOT true?
A
QJ QK

QR QS
B
JK QK

RS QS
C
QR QS

JK RJ
D
QR QJ

QS QK
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 12 of 29
2011-12
In the following diagram, it is given that C is the midpoint of BD ,
that AB  BD , and that BD  DE .
E
B
D
C
A
Prove ABC  EDC by selecting the most logical sequence of
statements and reasons.
Statements
1.
2.
3.
4.
5.
6.
7.
C is a midpoint of BD
BC  CD
BCA  ECD
AB  BD and BD  DE
ABC and EDC are right angles
ABC  EDC
ABC  EDC
Reasons
1. Given
2.
3.
4.
5.
6.
7.
Definition of Midpoint
Vertical angles are congruent
Given
_______________________
_______________________
_______________________
A
5. Perpendicular lines form four right angles
6. All right angles are congruent
7. Angle-Side-Angle (ASA)
B
5. Given
6. All right angles are congruent
7. Angle-Side-Angle (ASA)
C
5. Definition of congruent angles
6. All right angles are congruent
7. Side-Angle-Side (SAS)
D
5. Perpendicular lines form four right angles
6. Alternate interior angles are congruent
7. Right triangles are congruent to each other
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 13 of 29
2011-12
21
For what value of x is ABC ~ DEF ?
B
D
86°
A
A
B
C
D
22
10
4
C
F
2
2.1
2.5
4.125
Select all sets of given triangle lengths that would form a right
triangle.
I. 3, 4, 6
II. 8, 15, 17
23
E
86°
8
5
9
2x + 3
A
II, IV, V
B
II, III, V
C
I, V, VI
D
IV only
III.
IV.
11, 60, 61
5, 7, 12
V. 7, 24, 25
VI. 12, 15, 18
Which set of lengths could be the lengths of the sides of a
triangle?
A
B
C
D
1, 2, 3
6, 6, 14
7, 24, 25
10, 20, 33
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 14 of 29
2011-12
24
Roof trusses often use right triangles to make a flimsy 2 x 4 more
rigid to hold up the weight of the roof. If a house is 40 feet wide
and the roof is an isosceles triangle with base angles of 30
degrees, how far is it from the bottom edge of the roof to the
peak?
x
30°
30°
40 feet
25
A
40 3
ft
3
B
20 3
ft
3
C
20 3 ft _
D
40 ft
On a map, Richmond, Danville, and Charlottesville form a
triangle. Charlottesville is 85 miles from Richmond and Danville
is 100 miles from Richmond. Which is a possible distance
between Danville and Charlottesville?
A
B
C
D
5 miles
15 miles
150 miles
185 miles
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 15 of 29
2011-12
26
27
28
In scalene triangle ABC, mB  45o and mC  55o . What is the
order of the sides in length, from longest to shortest?
A
AB , BC , AC
B
BC , AC , AB
C
AC , BC , AB
D
BC , AB , AC
Pedro has a square practice net in his backyard. The diagonal of
the net is 6 feet. Find the length of one side of the net.
A
3 2 feet
B
2 3 feet
C
3 feet
D
12 feet
A surveyor is trying to determine the width of a river. He first
stands at point A, directly opposite a tree at point B. He then
walks 100 feet to point C. He measures the acute angle at point
C to be 79°. What is the width, w, of the river?
A
100 ft
C
79°
w
B
A
B
C
D
19.4 feet
101.87 feet
514.5 feet
524.1 feet
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 16 of 29
2011-12
29
From the top of a 210 foot tall lighthouse, the angle of
depression to a boat is 27 . Find the distance from the boat to
the base of the lighthouse.
A
B
C
D
95.3 feet
107 feet
187.1 feet
412.1 feet
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 17 of 29
2011-12
30
ABC and point E are shown in the diagram below.
y
E
A
C
x
B
Determine a possible location of point D to make ABC  CDE .
A
B
C
D
31
(2,
(4,
(3,
(4,
2)
1)
1)
2)
Given quadrilateral ABCD, where AB || CD , ABC  CDA , and a
diagonal AC . Which method can be used to prove ABC  CDA ?
A
B
C
D
Angle-Angle-Side (AAS)
Side-Side-Angle (SSA)
Side-Angle-Side (SAS)
Side-Side-Side (SSS)
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 18 of 29
2011-12
32
Scott wants to swim across a river that is 400 meters wide. He
begins swimming perpendicular to the shore he started from but
ends up 100 meters down river from where he started because of
the current. How far did he actually swim from his starting point?
A
B
C
D
300 m
387.3 m
412.3 m
500 m
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 19 of 29
2011-12
33
A tiled floor consists of a tessellating pattern of two regular
polygons. A portion of the tiled floor is shown below.
What two regular polygons are used in the tessellating pattern?
A
B
C
D
Octagons and Squares
Hexagons and Squares
Pentagons and Squares
Decagons and Squares
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 20 of 29
2011-12
34
In the drawing, ABCD is a parallelogram. What must be the
coordinates of the intersection of the diagonals?
y
D (a  c, b)
C (c, 0)
A
B
C
D
35
A (a, b)
B
x
a b
 , 
2 2
ac bc
,


2 
 2
ac b
, 

 2 2
ac b
, 

 2 2
The exterior angle of a certain regular polygon is 60°. How many
sides does the polygon have?
A
B
C
D
3
6
10
12
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 21 of 29
2011-12
36
A city park can be represented by trapezoid DEFG, where
DE || FG , and DF and EG represent hiking paths that span the
diagonals of the park.
A planning team is interested in planting additional trees
throughout the park and has measured some of the angles
between the edges of the park and the sidewalks as shown in the
diagram below to determine the best location for the trees.
D
E
24°
50°
36°
G
F
Using the information in the diagram, find mDFG .
A
B
C
D
24°
26°
36°
50°
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 22 of 29
2011-12
37
A spotlight, located at point S in the diagram below, illuminates
parts of a circular pond. Light is beamed at an angle of 25° from
»  40o .
the spotlight and intercepts the circle such that the m BC
A
B
25°
S
D
C
Find m јAD .
A
B
C
D
38
50°
65°
90°
115°
Rectangle QRST is shown.
Q
R
T
S
Which of the following would be a reason to claim that QRST is
NOT a square?
A
B
QS  RT
QT  QR
C
QT  TS
D
QR || TS
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 23 of 29
2011-12
39
In square ABCD, AC  3 x  4 and BE  x  6 , where E is the
intersection of the diagonals.
B
E
A
C
E
D
What is the length of AC ?
A
B
C
D
40
11
16
22
44
ABC is inscribed in circle O, and AB passes through O.
A
O
40°
B
C
If mBAC  40 , find m јAC .
A
B
C
D
40°
80°
100°
120°
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 24 of 29
2011-12
41
A circle has center (-2, 3) and radius 4 units. Which of the
following is a point on the circle?
A
B
C
D
42
(-2, 5)
(-2, -1)
(2, 7)
(-6, 7)
At Greg’s Greek Gourmet, diners have an opportunity to throw a
dart at a dartboard to earn a discount on their meal. The
dartboard is a circle with radius of 8 cm and is divided into two
sectors. Darts that land in the unshaded sector get a free meal,
and darts that land in the shaded sector get $5 off. The
dartboard is modeled by circle O below.
A
$5 off
O
B
FREE MEAL
C
»  135o , find the area of the dartboard that corresponds to
If mBC
a $5 discount.
A
B
C
D
6 cm 2
10 cm 2
24 cm 2
40 cm 2
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 25 of 29
2011-12
43
The coordinates of the endpoints of a diameter of a circle are
(6, 2) and (0, -2). Which of the following is an equation of the
circle?
A
B
C
D
44
x  32  y 2  13
2
x 2   y  3  13
x  32  y 2  52
2
x 2   y  3  52
In circle P, AD is a diameter and BC is perpendicular to AD at E.
If PD = 7 and AE = 4, find CE.
C
A
E
P
B
D
A
2 7
B
2 10
C
5.5
D
7
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 26 of 29
2011-12
45
46
47
Lea made two candles in the shape of right rectangular prisms.
The first candle is 15 cm high, 8 cm long, and 8 cm wide. The
second candle is 5 cm taller but has the same length and width.
How much additional wax was needed to make the taller candle?
A
320 cm3
B
640 cm3
C
960 cm3
D
1280 cm3
A tepee with a dirt floor in the shape of a right cone has a slant
height of 26 feet and a radius of 12.5 feet. Approximately how
much canvas would be needed to cover the tepee?
A
3730 sq ft _
B
4254 sq ft
C
1511 sq ft
D
1021 sq ft
The ratio between the volumes of two cubes is 125 to 216. What
is the ratio between their respective surface areas?
A
5:6
B
25:36
C
125:216
D
250:432
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 27 of 29
2011-12
48
Which of the following would triple the volume of the Egyptian
square-based Pyramid below?
A
B
C
D
49
add 3 to each dimension of the Pyramid
multiply every dimension of the Pyramid by 3
multiply only the height by 3
add 3 to the slant height
suur
suur
In circle P, TD and TB intersect at T. TA=10, TC=8, CD=12, and
AB=x+2. Find AB.
B
A
P
T
C
D
A
4
B
6
C
9.6
D
15
Geometry EOC SOL Simulation
Chesterfield County Public Schools
Page 28 of 29
2011-12
50
Which of the following three-dimensional shapes have equivalent
surface areas?
Figure 2
Figure 1
7 cm
Figure 4
Figure 3
A
B
C
D
Figures
Figures
Figures
Figures
1
2
3
1
and
and
and
and
Geometry EOC SOL Simulation
Chesterfield County Public Schools
2
3
4
4
Page 29 of 29
2011-12