Download Geometry EOC Practice Packet - Doral Academy Preparatory School

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EOC Review-
Week #1
3.
1. Given:k
II m II n
t
The conditional statement "all 45° angles
angles" is true. Based on this conditional
which of the following can be concluded
additional statement "the measure of LA
are acute
statement,
from the
is 45°"?
A
The complement of .LA is not an acute angle.
B
The supplement of LA is an acute angle.
C
LA is an acute angle.
D
LA is not an acute angle.
Which statement justifies the conclusion that
Ll == L2 == L3?
4.
Given mLRQS=!x+4,
and mL.RQT = 2x -
A If k II m II n and are cut by transversal t, then
alternate interior angles are congruent.
mLSQT=lx-6,
2
4
47.
What is m L.RQS ?
B If k II m II n and are cut by transversal t, then
vertical angles are congruent.
5
R
T
If k II m II n and are cut by transversal t, then
alternate exterior angles are congruent.
C
D If k II m II n and are cut by transversal t, then
corresponding angles are congruent.
Q
2.
What is the contrapositive of the statement below?
5.
Which statement is the inverse of the statement in
the box?
If a triangle is isosceles, then it
has two congruent sides.
If a quadrilateral is a rectangle,
then it is a parallelogram
A
B
If a triangle does not have two congruent sides,
then it is not isosceles.
A
If a quadrilateral is not a parallelogram, then it
is not a rectangle.
.
If a triangle is isosceles, then it does not have
two congruent sides.
B
If a quadrilateral is a parallelogram, then it is a
rectangle.
C
D
If a triangle has two congruent sides, then it is
isosceles.
C
If a quadrilateral is not a rectangle, then it is
not a parallelogram.
If a triangle is not isosceles, then it does not
have two congruent sides.
D
A quadrilateral is a rectangle if and only if it is
a parallelogram.
I
6.
L XYZ shown below has a measure of
(8x + 12)0.
(4x + 8)", and
The measure of Ll is
8.
7.
What is mLl?
20°
In the diagram, GH
G.s
and
L XYZ ?
y
B
= (3x-lO)"
mL3 = {2x+Sy
the measure of L2 is (9x _11)0.
What is the measure of
Given RSIITU, mL7
II IJ.
9.
A
145°
B
75°
C
35°
D
15°
6 7
5 8
R
2 3
T
14
U
/
In the drawing below, a II b with transversal t.
Using this information, what is the value of x?
~~--------~H
t
a
'-~~~-----------'b
F
If mLGLK
= 5Y
and mLEFJ = 120
J
0
,
what is
mLKEF?
A
8
A
55°
B
12
B
60°
C
34
C
65°
D 60
D 70°
Eoe Review - Week #:~
1.
3. M is the midpoint of RS, RM
MS = (4x - 2). What is RS?
In the diagram below, j .1m and k.l m.
m
A
20
B
17
=
(3x + 1), and
51
0
1
1
C 10
n
j
D 3
k
4. In the diagram below, PQ == MQ and mLM
What is m.dl'!
=
70 ~
P
A
39°
B
47°
C
51°
D
129°
T~M
Q
What is m LTQP?
2. In the figure below, wfbisects
LVWZ,
mLVWY= 32~ and mLVWX= 117~
v
I
w~----------~
A
70°
B
110°
C
140°
D
150°
5. According to the map, the road connecting the
cities of Oakton (0) and Ridgeton (R) intersects
the road cormecting Maple View (M) and Pineville
(P).
x
What is mLZWX?
C
42.5°
D
26.5°
If the roads intersect in the town of Forest Grove
(F), in the diagram, which statement is always
true?
M
A
MP=RO
B
PF.l OF
C
LOFP~LRFM
D LRFP=:LMFR
o
R
p
6.
IfE,
Given LABC is bisected by
mLABC = (6r-18), andmLABE = 36~
What is the value of r?
9.
OX is the bisector of LWOZ and OY is the bisector
of LXOZ.
Wi
A
15
B
30
C
36
D
72
y
z
If mLYOZ
7.
In the diagram, SR
~ what is mL'WOZ?
II UV.
100
se:-----------------.
0
T
= 26.5
B
79.5°
D
132.5°
R
1400
-------------~~
U
What is
V
mLSTU ?
10. In the drawing below, MN ~ JL.
M
I
___
----1-¥-
D 240°
K
I
N
8.
Given LP, LM = (3~ 1), MN
NP = (6x - 5), and LM =NP.
=
(4x - 3),
Which statement must be true?
••
------~.------~.~-----e
M
N
P
A
mLPKN
=
mLJKP
What is the length of MP?
B
mLPKN
=
90 + mLJKP
A
2
C
mLPKN
= 180 - mLJKP
B
7
D
mLPKN
=
C
12
D
19
L
270 - mLJKP
p
L
EOC
Review - Week #3
4.
1. ~MNOis shown below.
In the drawing, what is the measure of angle y?
v
M
12 in.
~n.
/
T
0
A
40
B
600
C
800
D
1000
/
z
N
28;n.~o
Which statement about this triangle is true?
2.
A
mLO >mLM
B
mLM >mLN
C
mLM <mLN
A
144
D
mLN <mLO
B
72'
C
36'
D
18'
5.
A triangle has side lengths of 10cm, 15cm, and
20cm. Which side lengths form the largest
angle?
6.
,
A
5 em, 10cm
BIOem,15cm
3.
C
10em,20em
D
15em,20em
The exterior angle of a base angle in an isosceles
triangle is 100 What is the measure of the vertex
angle?
0
•
C
800
D
600
7.
w
What is the measure of an angle that is four times
as large as its supplement?
0
8.
In the given figure, ED
of x?
II AE,
what is the value
10. Jill wants to measure the width of a river. She
marks the distances as shown in the diagram.
c
...------------- --..-......- ------......
D
B
~
9
x
E
~
C
E
River
B
i2yd
A
10yd
A
D
9.
A
12
B
13
C
14
D
15
Using this information, what is the approximate
width of the river?
Which parts must be congruent to prove ~PQR ~
APSR by SAS?
p
Q
R
A
LQ ~ LS and QP ~ SP
B
LQ ~ LS and QR~ SR
C
LQRP ~ LSRP and QP ~ SP
D
LQPR ~ LSPR and QP ~ SP
S
A
6.6 yards
B
10 yards
C
12.8 yards
D
15 yards
EOC Review - Week #4
1. In ~ABC, Z is the midpoint of AC and Y is
the midpoint of
4. In the figure given, what is the value of x?
Be .
A
2
B 6
C
12
D
14
""'-z
A
IfYZ = 21 and AB = (2x - 4), what is the
value of x?
5.
A 7.25
B
A right triangle is shown below.
What is the approximate measure of h?
12.5
A
100
B
115
C
140
D
173
C 23
200
D 46
2. Two angles are complementary. The measure
of one angle is 40° more than the other. Find
the measure of the larger angle.
6.
B
80°
C
110
How long is EF?
E
0
F
30 ft
20 ft
70ft
3.
Billy is 74 inches tall, and his shadow is 70 inches
long. What is the approximate angle of elevation
of the sun?
A
20 ft
B
25 ft
C
30 ft
D 35 ft
7.
9. While flying a kite, 400 ft of string was let out.
The string, when pulled tight, formed a 40°
angle with the ground. What was the
approximate
8.
In LJPQR,mL'Q is 3 times mLP, and mLR is 20
greater than mLP. What is mLP?
A
257 ft
B
306 ft
C
336 ft
D
400 ft
height of the kite?
10. KM is an altitude of lJJKL, and KM =JM The
measure of LLKMis 55°, and ML = 12 em.
C
50°
K
L-.
__
.__
...••••••.
~
M
What is the approximate length of JK?
A 8.4
B
11.9
C
20.7
D
24.2
L
soc Review-
Week #5
1. The angle of elevation from point G on the
I
3. Given BD.1 AC and D is the midpoint of AC.
ground to the top of a flagpole is 20°. The
height of the flagpole is 60 feet.
B
A-<-----~------"C
o
Which postulate would be used to prove
MBD == LJ.CBD?
Which equation could find the distance from point
G to the base of the flagpole?
A
. 200 =-x
SIn
60
B
. 200 =-60
SIn
x
C
60
tan 200 =x
D
tan20°
A
SSS Postulate
B
ASA Postulate
C
SAS Postulate
D
None of the above
4. A 20-foot ladder is leaning against a wall. The
foot of the ladder is 7 feet from the base of the
wall. What is the approximate measure of the
angle the ladder forms with the ground?
= 2..
60
A 70.7°
B 69.5°
2.
A mountain climber stands on level ground
C 20.5°
300 m from the base of a cliff. The angle of
elevation to the top ofthe cliff is 58°. What is
the approximate height of the cliff?
A
566m
5. What is true of a rhombus that is not true of all
other parallelograms?
B 480m
A
Opposite angles are congruent.
C 354 m
B
Diagonals are congruent.
C
Diagonals bisect each other.
D
Diagonals are perpendicular.
D 187 m
6. A ladder is leaning against the side of a
building. The ladder is 30 feet long, and the
angle between the ladder and the building is
15°. About how far is the foot of the ladder
from the building?
9. The angles of a quadrilateral are represented
by (9x -1) ~ (5x + 12)~ (6x -11) ~ and (4x)
0.
What is the value of x?
A
15
A 7.76 feet
B
12
B
8.04 feet
C
10
C
18.37 feet
D
7.5
D 28.98 feet
10. A dead tree was struck by lightning, causing it
to fall over at a point 10ft up from its base. If
the fallen treetop forms a 40° angle with the
ground, about how tall was the tree originally?
7.
8. Two sides of a square are represented by
x2 + 8x and 5x + 28. What is the
perimeter ofthe square?
A
13 ft
B
16 ft
C 23 ft
A
28
B
16
C
112
D
192
D 26 ft
Eoe Review-
Week #6
4. In a hexagon, three angles have the same measure.
The measure of each of the congruent angles is twice
the measure of the fourth angle and is half the
measure of the fifth angle. The sixth angle measure
115°. What is the measure of the smallest angle?
1. ABeD is a trapezoid with median EF .
What is the length of AB?
A 5 units
C
110°
B 7 units
C 9 units
D
10 units
5. Given the following figure composed of
regular polygons, find the value of x.
2. If KLMN is a rhombus, and m LKLM = 80° ,
what is the measure of Ll ?
A
40°
B
50°
L
B 108°
C
120°
D 132°
C 80°
D 90°
A 72°
N
3. The measure of each exterior angle of a
regular polygon is 45°. How many sides does
the polygon have?
6. JK and LM are perpendicular diameters of a circle.
They are each 12 inches long. What is the
approximate length of chord LK?
A 4
B
A
17 in
B
12 in
C
10.4 in
D
8.5 in
5
C 8
D 9
7. Figure JKLM is a parallelogram.
9. Given parallelogram EFGH, what is the length
of side EF?
3xl
E
M
l
What is the value of x?
H
B
55°
A
27
B
21
C
19
D
7
;
2x + 5
F
G
8. If PQRS is a rhombus, which statement must
be true?
R
5
P
Q
A
L PSR is a right angle.
B
PR==QS
C
LPQR
D
PQ==QR
== LQRS
10. A triangle has interior angles that measures 3x,
(2x + 15), and (x + 45). What is the measure
of the largest exterior angle?
EOC Review - Week #7
1. A sign is shaped like an equilateral triangle.
If one side of the sign is 36 inches, what is the
approximate area of the sign?
A
2.
3.
A regular octagon is inscribed in a circle. What is the
degree measure of each arc joining the consecutive
vertices?
4. In a trapezoid, the length of one base is 41 em and
the length of the median is 29 em. What is the
length of the other base?
2
1,296 in
B
A 12cm
c
B
14 em
D
C
15 em
D
17cm
In JKLM, JK is perpendicular to KL
JK
and
IIML.
5.
In the circle below, what is the value of x?
What is the area of the trapezoid?
A 120 sq em
A
B
144 sq em
C
164 sq ern
4 units
B 6 units
D
C
7 units
D
9 units
168 sq em
6.
Given ~RST - ~VUT. RT = 15, ST = 12,
TV = 45, and TY = 30. What is XT?
R
8. In circle 0, which term correctly identifies XY?
x s
45
A
chord
B
radius
C
secant
D
tangent
30
u
A
8
B
10
C
12
D
18
v
y
9.
To win a carnival game, Keisha must throw a dart
and hit one of25 circles in a dart board that is 4
feet by 3 feet. The diameter of each circle is 4
inches.
--4
feet
•
t
0 0 0 0 0 0
0 0 0 0 0 3feet
1 0 0
I
1000°
10
7. A circle is inscribed in a square as shown below.
-ltin
..-..
If a point is randomly chose inside the square,
what is the approximate chance that the point
lies outside the circle?
° 001
00
0
0 •
Approximately what is the probability that a
randomly thrown dart that hits the board would
also hit a circle?
A
18%
B
26%
C
63 %
D
73 %
A
21%
B
27%
C
73%
A
1,012 f(
D
79%
B
1,024 ft2
C
1,120 ft2
D
1,216 ft2
10. Find the area of the figure.
32 ft
Eoe Review
1.
- Week #8
What is the approximate area of the trapezoid?
3. IfmLP
=
measures
120°, what is the sum ofthe
of the remaining interior angles?
12cm
i
\scm
A 240°
C 720°
A
83 ern'
D 960°
B
110 em'
C
128 cnr'
D
192 crrr'
4. A right triangle is shown below. What is the
approximate value of x?
A
14.9
XO
2.
Marianna designed the logo shown for a
computer software company.
· /'
C
...•.
-/ /s
/ S
B
15.5
C
74.5
30
D 75.1
8
5. An apple pie is cut into six equal slices as
shown below.
If the diameter ofthe circle is 8 em, what is the
approximate area of the shaded part of the
logo?
2
B
50.24 cm
D
18.27 cm2
If the diameter of the pie is ten inches, what
is the approximate arc length of one slice
of pie?
A
1.67 in.
B
3.14 in.
C 5.24 in.
D 13.08 in.
6.
A gardener wants to enclose a circular garden
with a square fence, as shown below.
What is the approximate area ofthe shaded region?
If the circumference of the circular garden is
about 48 ft, which of the following is the
approximate length of fencing needed?
A
B
8.70 units'
A
31 ft
C
9.13 units"
B
61 ft
D
11.28 units2
C
122 ft
D 244 ft
7.
8.
9.
If Jim threw a marble inside the circle, what is the
probability that it would land inside the triangle?
A
0.08
B
0.15
C
0.31
A
D 0.61