Analytic Geometry Midterm Practice Exam
Name:
3.
If ^ABC is the original gure and ^A0 B0 C0
represents its dilation image, what is the center of
dilation?
…
1.
Date:
A0
A
What are the coordinates of point (2; 3) after a
translation to the left of 2 units and down 5 units,
and then a dilation by a factor of 1.5 about (0; 0)?
A.
( 6; 3)
B.
( 2; 1)
C.
(0; 1)
D. (0; 3)
C0
C
B

…

B0
(0; 0)
B.
(1; 3)
C.
(1; 2)
D. (2; 1)
4.
^ABC is the original gure and ^ A0 B0 C0
represents its dilation image. Fill in the blanks:
…
A.
A
^ABC is the original gure and ^A0 B0 C0
represents its dilation image. What is the center
of dilation?

…
…
B0
C0
B
C

C0
C
A0
A

^A0 B0 C0 is a dilation of ^ABC by a factor
about the point
.
of
…
B
B0

2.
A0
A.
(0; 0)
B.
(1; 3)
C.
(1; 2)
D. (2; 1)
page 1
A.
0.5; (0; 0)
B.
0.5; (4; 1)
C.
2; (0; 0)
D. 2; (4; 0)
5.
8.
^A0 B0 C0 , with vertices A0 (0; 0), B0 (0; 2) and
C0 (1:5; 3), is the image of ^ABC with vertices
A(0; 0), B(0; 4), and C(3; 6) under a dilation. If
the origin is the center of dilation, what is the
scale factor?
A.
0
B.
1
2
C.
The cones shown are not drawn to scale.
I.
2
D. unde ned
II.
6.
Under a dilation with center P and scale factor k,
A0 is the image of A. If PA = 7 and PA0 = 28,
what is the value of k ?
A.
1
4
B.
1
2
C.
4
III.
D. 8
IV.
7.
Based on the given information, which of the
cones are similar to one another?
Given the information in the diagram, do the
triangles have to be similar?
A.
Yes. The right triangle is 3 times the size of
the left triangle.
B.
Yes. All scalene triangles are similar
C.
No. Side c is not necessarily 24.
9.
D. No. Scalene triangles are never similar.
page 2
A.
I and III
B.
II and III
C.
II and IV
D. III and IV
If two isosceles triangles have congruent vertex
angles, then the triangles must be—
A.
congruent
B.
right
C.
equilateral
D. similar
Analytic Geometry Midterm Practice Exam
10.
11.
Which pair of triangles are always similar?
A.
2 scalene
B.
C.
2 isosceles
D. 2 obtuse
12.
Which of these statements, if true, is su cient to
prove that triangles STR and PQR are similar?
2 equilateral
1
2
A.
TQ =
C.
OS = OR
QR
B.
^PQR is isosceles
D. OS = OQPR
In the gure, OR = OC.
Which of these statements, if true, is su cient to
prove that triangles CAT and RAM are similar?
13.
A.
RA ? CM
B.
T is the midpoint of RA
C.
CA = 2 AM
D. CT + TA = RM + MA
page 3
Which of these statements, if true, is su cient to
prove that triangles LMN and NMO are similar?
A.
LN = 2 OM
B.
NO bisects LM
C.
OL = OO
D. OMLN = OMNO
Analytic Geometry Midterm Practice Exam
14.
Given:
PQ = PR
ST k QR
Prove:
^ PST is isosceles
Statement
15.
1. PQ = PR
given
3. ST k QR
given
2. mO1 = mO2
4. mO1 = mO3
Reason
Given that triangle ABC is similar to triangle DEC,
OABC corresponds to:
A.
OCDE
B.
ODEC
C.
OACB
D. OECD
5. mO2 = mO4
6. mO2 = mO3
7.
8. PS = PT
16.
9. ^PST is isosceles
In the proof, what is the reason for line 6?
A.
isosceles triangle theorem
B.
transitive property of equality
C.
corresponding Os are congruent
17.
Given that ^XYZ is similar to ^XDY, OXYD
corresponds to:
A.
OXZY
B.
C.
ODXY
D. ODYZ
OYXD
In the gure, DE k BC. Which proportion is not
true?
D. alternate interior Os are congruent
page 4
A.
AD AE
=
BA
CA
B.
AD
AB
=
AE
AC
C.
DB
BA
=
EC
CA
D.
AD
AE
=
DB AC
Analytic Geometry Midterm Practice Exam
18.
How many similar triangles are in the diagram?
A.
1
B.
2
C.
21.
3
D. cannot be determined
19.
20.
In the diagram, CD ? AC, BE ? AC, AB = 24,
BE = 18, and CD = 21. Find BC.
A.
4
B.
24
C.
30
D. 35
Based on this gure, how many similar triangles
can be identi ed?
B.
22.
A.
1
2
C.
3
D. cannot be determined
PQ is parallel to XY. What is the length of RX in
centimeters?
5 31
A.
6
B.
C.
3
D. 2
In the diagram, mOD = OE. Which of the
following statements are true for this diagram?
I.
^ADC
^BEC
II. ^ADC
^EBC
23.
III. AD k BE
A.
I only
B.
III only
C.
I and II
Determine the length of ST if MN is (8x
units.
D. I and III
page 5
A.
4x
2
3
B.
C.
4x +
3
2
D.
16x
8x
2
3)
6
3
Analytic Geometry Midterm Practice Exam
24.
26.
In the gure, k k ` k m k n. If AB = 4, AC = 10,
and EF = 6, then nd EG.
A.
15
B.
18
C.
12
D. 14
27.
25.
Given ^ABC
Which of the following is the correct mapping for
shape A to shape B?
^EDC.
A.
(x; y) ! ( x; y)
B.
(x; y) ! ( x; y)
C.
(x; y) ! (x; y)
D. (x; y) ! (x
3; y)
State the congruence relation for ^ABC and
^DEF.
A.
SSS
B.
SSA
C.
ASA
D. SAS
What is the value of y ?
A.
20
B.
5
C.
4
28.
D. 3
State the congruence relation for ^BWO and
^IRO. Use only the markings in the diagram.
A.
AAA
B.
SSA
C.
SAS
D. not necessarily congruent
page 6
Analytic Geometry Midterm Practice Exam
29.
State the congruence relation for ^XYZ and
^PQR.
31.
In the gure, FE = LS, mOYSL = mOHEF and
HE = YS. Complete the statement.
^FEH = ^
A.
ASA
B.
SSA
A.
YSL
B.
C.
SAS
C.
LEY
D. SYL
LSY
D. not necessarily congruent
30.
In the gure, mOT = mOV and E is the midpoint
of TV. What congruence statement proves
^TER = ^VEC ?
A.
SSS
B.
SAS
C.
ASA
D. not necessarily congruent
page 7
Analytic Geometry Midterm Practice Exam
32.
Which diagrams show that the two triangles must be congruent?
II.
I.
A.
33.
II only
B.
III.
I and II only
C.
Which congruency theorem is described below?
35.
“In two triangles, if two pairs of sides and their
included angles have equal measurement, then the
triangles are congruent.”
A.
SSS
B.
SAS
C.
ASA
I and III only
D. II and III only
The Corresponding Angles Conjecture states that
if two parallel lines are cut by a transversal, the
corresponding angles are congruent. The picture
below shows this relationship.
D. AAA
Which of these congruent angles are corresponding
angles?
34.
The SAS congruency axiom states that two
triangles are congruent if:
A.
two angles and the contained side of one
triangle are equal to two angles and the
contained angle of the other triangle.
B.
two sides and the contained angle of one
triangle are equal to two sides and the
contained angle of the other triangle.
C.
two angles and a side of one triangle are
equal to two angles and a side of the other
triangle.
A.
O1 and O4
B.
O1 and O 3
C.
O4 and O8
D. O4 and O 3
D. two sides and the excluded angle of one
triangle are equal to two sides and the
excluded angle of the other triangle.
page 8
Analytic Geometry Midterm Practice Exam
36.
38.
In the diagram, if mO8 = mO12, which two lines
(if any) must be parallel?
A.
kkm
B.
C.
kkmkn
D. none are parallel
Which of the following statements is not true?
mkn
A.
mODGC = mOJGK
B.
mOBCA = mODCG
C.
mOCGJ = mODGK
D. mOCJG = mOGJK
39.
37.
In the diagram, if lines a and b are parallel, which
of the following must be true?
A.
O7 = O1
B.
O3 = O6
C.
O3 = O5
D. O8 = O3
Given the diagram above, if mO6 = mO 5 and
mO19 = mO20, which of the following is true?
A.
line l and line a are perpendicular
B.
line a and line m are perpendicular
C.
line m and line b are perpendicular
D. line a and line c are parallel
page 9
Analytic Geometry Midterm Practice Exam
40.
Given:
WY is the angle bisector of OXWZ
41.
mOXYW = mOZYW
Prove:
statement
mOXWY = mOZWY
WY = WY
mOXYW = mOZYW
^WXY = ^ WZY
VY = WY
VX = WZ
Y is the midpoint of XZ
^WXY = ^WZY
WY is the O bisector of OXWZ
Given:
Prove:
^VXY = ^WYZ
reason
(1)
(2)
statement
(3)
Y is the midpoint of XZ
(4)
XY = YZ
(5)
VY = WY
In the above proof, what is reason (3)?
A.
sides opposite equal Os are equal
B.
de nition of a perpendicular bisector
C.
re exive property
reason
(1)
(2)
(3)
VX = WZ
^VXY = ^ WYZ
(4)
(5)
In the above proof, what is reason (2)?
D. de nition of a right angle
A.
de nition of angle bisector
B.
de nition of midpoint
C.
de nition of bisector
D. de nition of perpendicular bisector
page 10
Analytic Geometry Midterm Practice Exam
42.
Using the diagram, identify the dashed line
segment.
44. The drawing shows how to—
A.
construct an angle congruent to a given angle
B.
construct an equilateral triangle
draw an angle bisector
A.
median
C.
B.
altitude
C.
angle bisector
D. draw a perpendicular line through a point on
a line
D. perpendicular bisector
43.
Using the diagram, identify the dashed line
segment.
45.
The drawing shows how to—
A.
construct a parallel line through a given point
B.
draw a perpendicular bisector
copy a segment
A.
median
C.
B.
altitude
D. bisect an angle
C.
angle bisector
D. perpendicular bisector
page 11
Analytic Geometry Midterm Practice Exam
46.
The diagram shows a method for constructing
.
A.
a median in a triangle
B.
an angle bisector in a triangle
C.
an altitude of a triangle
49.
Given the triangle shown, which of the following
is true?
A.
sin B =
c
b
B.
cos A =
c
b
C.
tan A =
b
a
D. sin B =
b
c
D. the bisector of the base
50.
47.
Which of the following ratios is the tangent of an
angle?
A.
opposite
hypotenuse
B.
hypotenuse
adjacent
C.
adjacent
hypotenuse
D.
opposite
adjacent
Which of the following ratios is equivalent to
A.
sin S =
3
5
B.
cos S =
4
5
C.
tan S =
5
4
D. ^PRS is a right triangle
51.
48.
Which of the following statements is incorrect for
the given diagram?
1
?
cos
Identify the statement that is incorrect.
A.
sin y =
a
b
B.
cos y =
c
b
tan y =
a
c
A.
hypotenuse
adjacent
B.
adjacent
hypotenuse
C.
C.
hypotenuse
opposite
D.
opposite
adjacent
D. tan (90
page 12
y )=
a
c
Analytic Geometry Midterm Practice Exam
52.
Which of the following statements is incorrect?
A.
cos 25 =
19
x
B.
cos 25 =
y
x
C.
tan 25 =
19
y
55.
In ^DEF, which of the following is equal to
A.
sin D
B.
C.
cos D
D. tan D
5
12 ?
sin E
D. 361 + y2 = x2
56.
If sin OA =
A.
53.
Given the following triangle, sin =
A.
3
5
B.
4
5
C.
4
3
D.
5
3
.
57.
Given the triangle XYZ, what is cos Z?
A.
8
17
B.
15
17
C.
17
15
D.
17
8
58.
B.
3
4
C.
7
5
C.
12
13
In the triangle below, sin P =
5
13 .
A.
page 13
and cos OA = 54 , what is tan OA?
D.
1
5
The sides of a right triangle are 5, 12, and 13.
The sine of the smallest angle is
A.
54.
4
3
3
5
5
12
12
13
B.
B.
5
13
5
12
C.
13
12
D.
13
5
Find cos R.
D.
5
13
Analytic Geometry Midterm Practice Exam
59.
For the triangle shown, mOB = 90 and cos C =
What is cos A?
A.
60.
15
8
If sin =
B.
2
3
8
15
C.
15
17
, then what are the cos
61.
If sin =
2
5
62.
If sin P =
x
and O P is acute, then:
3
, then what are the cos
D.
64. Find the length of side x.
15
17 .
A.
12
B.
14
C.
144
D. 194
8
17
65.
and tan ?
In the diagram, AB = 15, DB = 6, and BC = 8.
If mOB = 90 , what is the perimeter of triangle
ADC ?
A.
24
B.
36
C.
42
D. 60
and tan ?
a) what is cos P ?
b) what is tan P ?
63.
If sin P =
66.
Find b.
A.
16
B.
26
C.
76
D. 104
x
and O P is acute, then:
5
a) what is cos P ?
b) what is tan P ?
page 14
Analytic Geometry Midterm Practice Exam
67.
68.
Find a.
69.
A.
18.4
B.
26
C.
36.8
D. 52
70.
In triangle RST, RS = 9 and mOR = 40 , nd the
length of ST to the nearest tenth.
A.
5.8
B.
14.1
C.
31
D. 4
page 15
Solve for the altitude a in terms of x.
A.
p
3 x
B.
C.
p
x 2
2
D.
p
3 2
2
p
x 3
2
In the triangle shown, determine OA to the nearest
degree.
A.
22
B.
32
C.
40
D. 58
Analytic Geometry Midterm Practice Exam
Problem-Attic format version 4.4.218
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Licensed for use by [email protected]
Terms of Use at www.problem-attic.com
Analytic Geometry Midterm Practice Exam
03/09/2015
1.
Answer:
Objective:
B
G.SRT.1A
15.
Answer:
Objective:
B
G.SRT.5
2.
Answer:
Objective:
D
G.SRT.1A
16.
Answer:
Objective:
A
G.SRT.5
3.
Answer:
Objective:
D
G.SRT.1A
17.
Answer:
Objective:
D
G.SRT.5
4.
Answer:
Objective:
A
G.SRT.1A
18.
Answer:
Objective:
C
G.SRT.5
5.
Answer:
Objective:
B
G.SRT.1B
19.
Answer:
Objective:
D
G.SRT.5
6.
Answer:
Objective:
C
G.SRT.1B
20.
Answer:
Objective:
A
G.SRT.5
7.
Answer:
Objective:
C
G.SRT.2
21.
Answer:
Objective:
A
G.SRT.5
8.
Answer:
Objective:
A
G.SRT.2
9.
Answer:
Objective:
22.
Answer:
Objective:
C
G.SRT.5
D
G.SRT.3
10.
Answer:
Objective:
23.
Answer:
Objective:
D
G.SRT.5
B
G.SRT.3
11.
Answer:
Objective:
24.
Answer:
Objective:
A
G.SRT.5
A
G.SRT.4
12.
Answer:
Objective:
25.
Answer:
Objective:
B
G.SRT.5
D
G.SRT.4
13.
Answer:
Objective:
26.
Answer:
Objective:
C
G.CO.6
D
G.SRT.4
14.
Answer:
Objective:
27.
Answer:
Objective:
A
G.CO.7
B
G.SRT.4
Teacher's Key
28.
Answer:
Objective:
C
G.CO.7
43.
Answer:
Objective:
D
G.CO.12
29.
Answer:
Objective:
D
G.CO.7
44.
Answer:
Objective:
A
G.CO.12
C
G.CO.7
45.
Answer:
Objective:
A
G.CO.12
31.
Answer:
Objective:
B
G.CO.7
46.
Answer:
Objective:
C
G.CO.12
32.
Answer:
Objective:
D
G.CO.7
47.
Answer:
Objective:
D
G.SRT.6
33.
Answer:
Objective:
B
G.CO.8
48.
Answer:
Objective:
A
G.SRT.6
34.
Answer:
Objective:
B
G.CO.8
49.
Answer:
Objective:
D
G.SRT.6
35.
Answer:
Objective:
C
G.CO.9
50.
Answer:
Objective:
C
G.SRT.6
36.
Answer:
Objective:
B
G.CO.9
51.
Answer:
Objective:
D
G.SRT.6
37.
Answer:
Objective:
B
G.CO.9
52.
Answer:
Objective:
A
G.SRT.6
38.
Answer:
Objective:
D
G.CO.9
53.
Answer:
Objective:
B
G.SRT.6
39.
Answer:
Objective:
A
G.CO.9
54.
Answer:
Objective:
B
G.SRT.6
40.
Answer:
Objective:
C
G.CO.10
55.
Answer:
Objective:
D
G.SRT.6
56.
Answer:
Objective:
B
G.SRT.6
57.
Answer:
Objective:
B
G.SRT.6
58.
Answer:
Objective:
D
G.SRT.7
30.
Answer:
Objective:
41.
Answer:
Objective:
B
G.CO.10
42.
Answer:
Objective:
C
G.CO.12
Page 2
Teacher's Key
59.
Answer:
Objective:
D
G.SRT.7
60.
p
Answer:
cos =
Objective:
G.SRT.7
61.
p
Answer:
cos =
Objective:
G.SRT.7
62.
p
Answer:
5
and tan =
3
9
x2
Objective:
3
G.SRT.7
63.
p
21
and tan =
5
; p
x
9
x2
Objective:
25 x2
x
; p
5
25 x2
G.SRT.7
64.
Answer:
Objective:
A
G.SRT.8
65.
Answer:
Objective:
B
G.SRT.8
66.
Answer:
Objective:
B
G.SRT.8
67.
Answer:
Objective:
B
G.SRT.8
68.
Answer:
Objective:
A
G.SRT.8
69.
Answer:
Objective:
D
G.SRT.8
70.
Answer:
Objective:
C
G.SRT.8
Answer:
2
p
5
2
p
21
Page 3