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GEOMETRY- Sem 2 FINAL StudyGuide
NOTE: This exam contains many diagrams and figures. Do not assume that diagrams are
drawn to scale.
1.
2.
Given:
. Which of the following must be true?
A
E   Q
C
B
DE  PQ
D
mP  mD  180
ABC ~ DEF according to which similarity theorem?
A
C
AA similarity
F
B
SAS similarity
18
18
C
ASA similarity
D
SSS simiilarity
6
D
3.
A
B
27
6
9
Choose the reason that justifies the statement, “The following polygons are similar.”
3
6
1
1
2
2
2
4
A
B
C
D
4.
Consecutive angles are congruent, and the bases are parallel.
Opposite angles are congruent, and the corresponding legs are congruent.
Corresponding angles are congruent, and the bases are parallel.
Corresponding angles are congruent, and the measures of corresponding sides
are proportional.
In the diagram shown below, what are the values of x and y?
x
y
[Hint: use proportion to solve for the variable]
16
3
2
4
6
Diagram not to scale.
1
E
M
5.
If QMT~XYZ , complete the proportion: QT = _?_
XZ
YZ
A
MT
C
QM
B
XY
D
Q
T
Y
QT
X
Z
6.
A man 6 feet (ft) tall is standing 4 ft from the base of a flagpole. If the shadow that he
makes on the ground is 10 ft long, how tall is the flagpole? (See the diagram below)
A
2.4 ft
C
8.4 ft
B
6.33 ft
D
10 ft
?
6
ft
10 ft
4 ft
7.
What is the value of x in the diagram shown below?
Diagram not to scale.
3
5
5
8.
x
In circle O, measure of arc AC is 90 degree.
What is m  ABC?
B
A
O

90
9.
C
In circle C, m  ACE = 40°.
What is the measure of arc AE?
C
A
A
E
10.
?
If tangents AB and BC form minor BC measuring 130˚,
find mBAC in the diagram shown.
B
130˚
C
2
C
B
11.
In circle O, AC is a chord, perpendicular to diameter
BD . If AE = 7, and ED = 16, find the length of EC.
E
7
A
12.
O
16
D
In circle B, find the length of AD .
B
12
15
A
D
13.
In circle O, AB and BC are tangent. Find the value of x.
24
A
B
7
3x
O
C
14.
B
What is mBEC in the diagram shown?
A
120
E
80
C
D
15.
What is the length of the diagonal of this square?
7 cm
16.
What is the length of side b in the triangle shown?
4 2
b
17.
Given  ABC is equilateral, what is AB?
A
30
8 3
C
3
60
B
18.
What is the polygon that has 12 sides? 10 sides? 8 sides? 6 sides? 5 sides?
19.
What is the value of x in the quadrilateral shown?
68
72
20.
A
C
B
D
The sum of the interior angles of a regular polygon is 1080 . How many sides does
the polygon have?
(Note: the sum of the interior angles of a regular polygon with n sides is (n  2)180 )
A
21.
x
115
C
B
D
For circle O, which of the following statements is NOT correct?
A
A
B
C
D
AE
AD
DB
DC
is a tangent line.
is a chord.
is a radius.
is a secant line.
E
B
D
O
C
22.
Using the right triangle below, which set of trigonometric ratios are equal?
B
10
6
A
C
8
A
B
23.
sin A, sin B
cos A, cos B
C
D
sin A, cos B
none are equal
Which of the following equations can be used to find the length of side a in the triangle
shown below?
B
20
a
A
42
C
b
B
13
24.
Write a fraction to find cos A , sine A, and tan A?
4
5
C
12
A
Use the following table to answer questions 25 and 26.
Angle A
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
25.
Sin A
.5736
.5878
.6018
.6157
.6293
.6428
.6561
.6691
.6820
.6947
.7071
.7193
.7314
.7431
.7547
.7660
.7771
.7880
.7986
Cos A
.8192
.8090
.7986
.7880
.7771
.7660
.7547
.7431
.7314
.7193
.7071
.6947
.6820
.6691
.6561
.6428
.6293
.6157
.6018
Tan A
.7002
.7265
.7536
.7813
.8098
.8391
.8693
.9004
.9325
.9657
1.000
1.036
1.072
1.111
1.150
1.192
1.235
1.280
1.327
A rope 50 feet in length is stretched from the ground to the top of a building which is 40
feet away. Which is the best estimate for the angle of elevation that the rope makes with
the ground (x)?
50 ft
x
40 ft.
26.
A boy flies a kite with a string 100 meters long. The kite string makes an angle of 40 
with the ground. How high above the ground from point P is the kite?
?
100 m
40
P
27.
1
a  P , what is the area of a regular hexagon with an apothem
2
of length 3.5 inches (in) and a side of 4 inches? (see diagram)
Using the formula A 
5
4
in
3.5
in.
28.
The goal area on a basketball court consists of a rectangle, with a
semi-circle at the top, as shown. What is the area
of the figure?
20
ft.
12 ft
29.
What is the area of the trapezoid shown? (Note: A =
1
h(b1  b 2 ) )
2
5 ft.
6 ft.
4 ft.
30.
If the area of a circle is 100 , what is the radius?
31.
A circle has circumference = 16 cm . What is the area?
32.
Which of the following gives the equation of a circle with radius = 5, and center at
(2, –3)?
A
B
33.
(x  2)2  (y  3)2  10
(x  2)2  (y  3)2  10
(x  2)2  (y  3)2  25
C
D
(x  2)2  (y  3)2  25
Find the total surface area of a right pyramid with a square base
when each edge of the base is 2 ft. and the slant height is 6 ft.
(S  1 Pl  B)
6 ft.
2
.
34.
2 ft.
Find the volume the cone with a radius of 3 inches and a height of 10 in.
1
(V =  r 2 h )
3
10
in
3 in
35.
A new soda can is being designed to be taken on a space shuttle mission. The can
will be cylindrical, 6 cm. in diameter and 20 cm. in height (see figure). What
will the volume of the can be? (V =  r 2 h )
6 cm
20
cm
6
36.
A soup container is in the shape of a right cylinder, with base radius = 3 cm, and height
6 cm. Find the total surface area of the container. (S = 2 r 2  2 rh )
3cm
Answer: ________ π cm2
37.
6cm
What is the area of a kite with diagonals measuring 10cm and 8 cm?
10 cm
8cm
38.
What is the volume of the triangular prism? (V=Bh)
5ft
4 ft.
10 ft.
6 ft.
39.
A ball, in the shape of a sphere, has a radius of 6 cm. Find the
surface area of the ball. (Note: surface area of a sphere = 4 r 2 )
Answer: ________ π cm2
6cm
40.
How much steel is required to make a solid ball bearing (in the shape of a sphere) with
4
diameter 8 in.? (Note: volume of a sphere =  r 3 )
3
Answer: ________ π cm3
8in
41.
If A(2, -4) is reflected across the x-axis, what tare the coordinates of the image, A’ ?
42.
Given: Triangle ABC formed by A(2,1), B(3,6), C(-1, 10). Give the coordinates of
∆A’B’C’, what is the coordinates of the image under the translation
7