Download 1. Any triangle may be rotated and translated so that one vertex is at

GeometryRegularSemester1Review 2015–2016
1. Any triangle may be rotated and
translated so that one vertex is at the
origin and another vertex is on the
positive x-axis. What is the
relationship between the length of 𝐷𝐸
one of the triangle's midlines, and the
length of 𝐵𝐶?
3. If ∠𝐴𝐸𝐵 = 2𝑥 + 32 and ∠𝐷𝐸𝐶 =
!
𝑥 + 65 what is the value of 𝑥?
!
A. −22
B. 19.5
C. 22
D. 58
4.
!
A. 𝐷𝐸 = ! 𝐴𝐶
B.
!"
!"
!"
= !"
!
If line r and s are parallel, then all of
the following statements are valid
conclusions except:
C. 𝐷𝐸 = ! 𝐵𝐶
!
D. 𝐷𝐸 = ! 𝐴𝐵
A. ∠3 ≅ ∠7
B. ∠1 ≅ ∠5
C. ∠1 ≅ ∠ 7
D. ∠3 ≅ ∠6
2. Find the length of 𝐻𝐼.
8x+5
H
A. 4
C. 19
2x+10
I
B. 18
D. 37
3x+7
J
5. Point A has the coordinates (2, 5).
Point B has the coordinates (6, 17).
How long is segment 𝑨𝑩 in simplified
radical form?
A. 160
C. 16 10
B. 48
D. 4 10
Fall2015
GeometryRegularSemester1Review 2015–2016
6. Select all undefined terms from the
below list.
I. Point
IV. Plane
II. Ray
V. Line
III. Segment
VI. Angle
A.
B.
C.
D.
9. Raymond threw a ball that bounced
up at an angle of (2x +4). What is the
value of x?
I, II, IV, V
I, II, V
I, IV, V
I, III, IV, V
7. Marcy made the following statement:
“If two lines are parallel, then they
have the same slope.”
Which of the following is a correct
analysis of Marcy’s statement?
A. Marcy’s statement is true.
B. Marcy’s statement is false. The
slopes of the lines are negative
reciprocals.
C. Marcy’s statement is sometimes
true.
D. Marcy’s statement is false, but the
converse is true.
3x+6
2x+4
A. 16
B. 36
C. 45
D. 54
10. 𝐴𝐵 ∥ 𝐶𝐷 Find 𝑚∠𝐴𝐵𝐶
B
10x-30
A
8. Find the contrapositive of the
following statement:
“If Jack plays baseball, then Jack
participates in sports.”
A. If Jack participates in sports, then
Jack plays baseball.
B. If Jack does not play baseball, then
Jack does not participate in sports.
C. If Jack does not play baseball, then
Jack participates in sports
D. If Jack does not participate in
sports, then Jack does not play
baseball.
D
5x+5
C
A. 7
B. 40
C. 140
D. 180
Fall2015
GeometryRegularSemester1Review 2015–2016
11. Which graph best represents a line
parallel to the line with the equation
𝑦 = −3𝑥 − 2 ?
12. A line passes through point (6, −3)
!
with a slope of !.
Write the equation of the line in slopeintercept form.
!
A. 𝑦 = − ! 𝑥 − 7
!
B. 𝑦 = − ! 𝑥 + 7
!
C. 𝑦 = ! 𝑥 + 7
!
D. 𝑦 = ! 𝑥 – 7
A.
13. 𝑷𝑸𝑹𝑺 is translated 6 units to the right
and 4 units up. What are its new
coordinates?
B.
C.
D.
A. 𝑃 (−3, −1), 𝑄(0, −1), 𝑅(0, −4), 𝑆(−3, −4)
B. 𝑃 (−6,1), 𝑄(−3,1), 𝑅(−3, −2), 𝑆(−6, −2)
C. 𝑃 (0,1), 𝑄(3,1), 𝑅(3, −2), 𝑆(0, −2)
D. 𝑃 (0, −3), 𝑄(3, −3), 𝑅(3, −6), 𝑆(0, −6)
14. Classify the triangle with vertices at
the following coordinates R(−2, −2),
S(1, 4), T(4, −5).
A. Scalene
B. Isosceles
C. Equilateral
D. Not enough Information
Fall2015
GeometryRegularSemester1Review 2015–2016
15.
The Missing statements are listed below, but they are out of order.
Statement R: ∆𝐋𝐌𝐍 ≅ ∆𝐐𝐏𝐍 (Angle-Side-Angle ≅)
Statement S: ∠𝟐 ≅ ∠4 (Alternate Interior Angles)
Statement T: 𝑳𝑵 ≅ 𝑸𝑵 (Corresponding Parts of ≅ ∆′𝑠)
What is the correct order for these statements to be placed in the proof above?
A. Statement S, Statement T, Statement R
B. Statement R, Statement S, Statement T
C. Statement R, Statement T, Statement S
D. Statement S, Statement R, Statement T
Fall2015
GeometryRegularSemester1Review 2015–2016
16.
18.
Based on the drawing, which of the
following rules could be used to prove
∆ UVW≅ ∆𝑋𝑌𝑊?
To show ∠𝐁𝐃𝐄 ≅ ∠𝐂𝐓𝐎 using
Corresponding Parts of Congruent
Triangles are Congruent, which of the
following would you need to prove?
A. ∠𝐶𝑂𝑇 ≅ ∠𝐵𝐸𝐷
B. 𝑂𝑇 ≅ 𝐸𝐷
C. ∠𝐷𝐵𝐸 ≅ ∠𝑇𝐶𝑂
D. ∆𝐶𝑂𝑇 ≅ ∆𝐵𝐸𝐷
A. Hypotenuse–Leg
B. Side-Angle-Side
C. Angle-Side-Angle
D. Side-Side-Side
19.
17.
Which set of given information does
not prove ∆𝐶𝐴𝑀 ≅ ∆𝐶𝑂𝑀?
∆𝑨𝑩𝑪 is isosceles, where 𝑨𝑩 ≅ 𝑩𝑪.
A. ∠MCA ≅ ∠𝑀𝐶𝑂,
∠CAM ≅ ∠COM
If 𝑚∠𝐴 = 5𝑥 + 30 and 𝑚 ∠𝐵 = 2𝑥,
then find 𝑚∠𝐶.
B. 𝐴𝐶 ≅ 𝑂𝐶,
∠ACM ≅ ∠OCM
C. 𝐴𝐶 ≅ 𝑂𝐶,
∠CAM ≅ ∠𝐶𝑂𝑀
A. 180°
B. 80°
C. 20°
D. 10°
D. 𝐶𝐴 ≅ 𝐶𝑂,
𝐴𝑀 ≅ 𝑂𝑀
Fall2015
GeometryRegularSemester1Review 2015–2016
20. What are the coordinates of the image
of the point (−4, 12) under a dilation
with a scale factor of 4 and the center
of dilation at the origin?
A. (−1, 3)
B. (−16, 12)
C. (−16, 48)
D. (8, 48)
21. What is the measure of ∠𝑃 in the
figure shown here?
24.
B
4
5
A
6
C
4
List the angles in order from smallest
to largest.
A. ∠𝐴, ∠𝐵, ∠𝐶
B. ∠𝐵, ∠𝐶, ∠𝐴
C. ∠𝐶, ∠𝐴, ∠𝐵
D. Not enough information
25. Each side of a square is 80 units. Find
the length of the squares’ diagonal.
A.
B.
C.
D.
33°
48°
57°
66°
22. To locate the _________________ of a
triangle, you can construct the
medians of each side of the triangle.
A. Centroid
B. Circumcenter
C. Circumcircle
D. Incenter
A. 80
B. 40
C. 80 2
D. 40 2
23. To locate the _________ of a triangle, you
can construct the perpendicular
bisector of each side of the triangle.
A. Circumcenter
B. Incenter
C. Median
D. Circumcircle
Fall2015
GeometryRegularSemester1Review 2015–2016
26. In ∆𝐷𝐸𝐹, DE = 7 cm and EF = 12 cm.
Which of the following could be a
possible length of DF?
28. Figure ABCD is a kite.
A
E
7
cm
D
A.
B.
C.
D.
93°
12
cm
D
F
5 cm
10 cm
19 cm
24 cm
B
100°
C
Find 𝑚∠𝐶.
A. 32° B. 67° C. 93° D. 100°
27.
29. Each of the following statements
about similar pentagons DEFGH and
JKLMN is true except:
E
11
13
D
F
What is the classification of the
triangle?
A. Acute
B. Right
C. Obtuse
D. Not enough information
A. The ratio of the corresponding sides
of pentagons DEFGH and JKLMN is
2:1.
B. Pentagon DEFGH I twice as big as
pentagon JKLMN.
C. Both pentagons have corresponding
angles that are congruent.
D. Pentagon JKLMN is the result of a
translation of pentagon DEFGH.
Fall2015
GeometryRegularSemester1Review 2015–2016
30. The two trapezoids in the figure are
similar, with 𝑨𝑩𝑪𝑫~𝑳𝑴𝑱𝑲. If the
lengths of sides 𝐵𝐶, 𝐶𝐷, and 𝐽𝑀 and
are known, then what is the other side
length that can be determined using a
proportion?
32. Desiree is designing two flowerbeds
for her backyard. The flowerbeds are
to be similar rectangles. The length of
the larger bed will be 8ft and the
length of the smaller bed will be 4 ft.
Desiree wants the width of the larger
bed to be 5ft. For the flowerbeds to be
similar, what should be the width of
the smaller bed?
A.
B.
C.
D.
A. AB
C. KL
𝑤
𝑤
𝑤
𝑤
=
=
=
=
2.5ft
5ft
10ft
13ft
B. JK
D. ML
33.
31. The two trapezoids in the figure are
similar, with 𝑨𝑩𝑪𝑫 ~ 𝑳𝑴𝑱𝑲.
If 𝑨𝑩 = 𝟏𝟎, 𝑨𝑫 = 𝟏𝟐, 𝑪𝑫 = 𝟖
and 𝑳𝑲 = 𝟏𝟖 what is LM?
An equilateral triangle is contained
within the isosceles trapezoid shown
above. What is the measurement of
the largest angle within this diagram
(ignoring the straight angle)?
A.
B.
C.
D.
12
15
21.6
27
A.
B.
C.
D.
120°
110°
100°
60°
Fall2015
GeometryRegularSemester1Review 2015–2016
34. What is the missing property of
equality for the algebraic proof?
Statements
Reasons
1. 4𝑥 − 7 = 2𝑥 + 3
1. Given equation
2. 2𝑥 − 7 = 3
2. Subtraction Property
3. 2𝑥 = 10
3. ________________________
4. 𝑥 = 5
4. Division Property
A. Addition Property
B. Multiplication Property
C. Reflexive Property
D. Substitution Property
35. Triangle PQR has vertices at 𝑷 −3, 3 ,
𝑸 −3, −2 and 𝑹 −1, −2 . This
triangle is transformed to make
∆𝐏 ! 𝐐! 𝐑! , as shown.
36. Rectangle 𝑹𝑪𝑻𝑮 has two of its
vertices at 𝑹(−2,3) and 𝑪(−2, −1).
Which of the following could be the
coordinates for the other two vertices
of this rectangle?
A. 𝑇 (5, 2) and 𝐺 (5, 6)
B. 𝑇 (−2, 4) and 𝐺 (−2, 8)
C. 𝑇 (5, −1) and 𝐺 (5, 3)
D. 𝑇 (−2, −3) and 𝐺 (−2, 7)
37. What is 𝑚∠𝐷?
A. 30
B. 60
C. 90
D. 120
If this transformation is a reflection,
then what are the coordinates for
point R'?
A. 1, −2
B. 1, 3
C. (5, −2)
D. (5, 3)
Fall2015
GeometryRegularSemester1Review 2015–2016
38. Quadrilateral ABCD has vertices at
𝑨(2,6), 𝑩(4,2), 𝑪(6,4) and 𝑫(5,6). The
x- and y-coordinates of each of these
points are multiplied by −1.5 to create
a similar quadrilateral in Quadrant III.
39. In Geometry class, students are using
parallelograms that have been cut out
of construction paper. Using one of
these paper shapes, a student tears
two consecutive corners from a
parallelogram.
Which similarity statement best
describes the relationship between
these two figures?
Which best describes the relationship
between these two corners that have
been removed from the
parallelogram?
A.
B.
C.
D.
ABCD~MGRT
ABCD~TRGM
ABCD~GRTM
ABCD~GMTR
A.
B.
C.
D.
Fall2015
GeometryRegularSemester1Review 2015–2016
40. In triangle ABC, 𝑚∠𝐴 = 𝑥 − 30 °,
𝑚∠𝐵 = 2𝑥 − 80 °, and 𝑚∠𝐶 =
𝑥 − 70 °. What kind of triangle is
∆ABC?
A.
B.
C.
D.
Acute scalene
Equilateral
Obtuse scalene
Right scalene
43. What is the value of x?
10 cm
13 cm
x cm
A.
B.
C.
D.
41.
7
3
23
16
44. What is the midpoint of A(–2, 5) and
B(7, –3)?
A.
B.
C.
D.
In ∆ABC, M and N are midpoints of
sides. Which statement best describes
the relationship between
MN and AC in ∆ABC?
45. If M is the midpoint of 𝐿𝑁 for L(–3, 4)
and M(1, –2), what are the
coordinates of N?
A.
B.
C.
D.
!
A. MN = ! AC
B. AC = 2MN
C. MN ∥ AC
D. All of the above
42. What is the value of x?
(4.5, 1)
(2.5, 1)
(2.5, 4)
(5, 2)
(–1, 1)
(5, –8)
(4, –6)
(–2, 2)
46. How many lines of symmetry in the
regular polygon below?
(3x)°
(2x – 5)°
A.
B.
C.
D.
30
20
5
37
(4x + 25)°
A. 2
C. 6
B. 3
D. 12
Fall2015
GeometryRegularSemester1Review 2015–2016
47. Choose from the below reasons to
complete the proof.
48. Which value of x makes ℓ! ∥ ℓ! ?
A. Linear Pair Theorem
B. Addition Property
C. Subtraction Property
D. Definition of supplementary
E. Reflexive Property
F. Substitution Property
G. Triangle Sum Theorem
H. Symmetric Property
(4x – 5)°
(5x + 5)°
ℓ!
ℓ!
ℓ!
A.
B.
C.
D.
5
30
10
20
Given: ∠1, ∠2 and ∠3 are interior angles of a
triangle and exterior angle ∠4
1
Prove: 𝑚∠1 + 𝑚∠2 = 𝑚∠4
2
Statements
1. 𝑚∠1 + 𝑚∠2 +
𝑚∠3 = 180°
Reasons
1.
2. ∠3 𝑎𝑛𝑑 ∠4 are
supplementary
2.
3. 𝑚∠3 + 𝑚∠4 = 180°
3.
4. 𝑚∠1 + 𝑚∠2 +
𝑚∠3 = 𝑚∠3 + 𝑚∠4
4.
5. 𝑚∠1 + 𝑚∠2 = 𝑚∠4
5.
3 4
49. Determine which if the below
statements are true.
I.
II.
III.
IV.
A.
B.
C.
D.
All squares are rhombi.
All parallelograms are rectangles.
All kites are quadrilaterals.
All trapezoids are parallelograms.
I only
I and II
I and III
II and IV
50. Which type of transformation does
NOT result in a rigid motion?
A.
B.
C.
D.
Dilation
Reflection
Rotation
Translation
Fall2015
GeometryRegularSemester1Review 2015–2016
51. What is the value of x in the
trapezoid?
54. Which property justifies that
𝑃𝑅 ≅ 𝑃𝑅?
Q
105°
R
P
x°
A.
B.
C.
D.
S
105
75
180
85
A.
B.
C.
D.
52. Given 𝑚∠𝑃𝑄𝑅 = 120°, what is
𝑚∠𝑃𝑄𝑆 ?
Transitive
Symmetric
Reflexive
Reflective
55. Which of the following lengths of
triangles can be classified as obtuse?
S
P
(9x + 5)°
Q
A.
B.
C.
D.
R
(2x + 5)°
10
25
90
95
A.
B.
C.
D.
8 cm, 15 cm, 17 cm
9 cm, 12 cm, 14 cm
13 cm, 14 cm, 18 cm
15 cm, 20 cm, 26 cm
56. How many distinct line segments exist
in the figure below?
53. Quadrilateral ABCD is formed with
A(1, 2), B(3, 5), C(6, 3), and D(3, 0).
Which could be used to prove that
∠𝐴𝐵𝐶 is a right angle?
!
A. The slope of 𝐴𝐵 is !, and the slope
!
of 𝐵𝐶 is !. They are equal.
!
B. The slope of 𝐴𝐵 is !, and the slope
!
of 𝐵𝐶 is − !. They are opposite
reciprocals.
!
C. The slope of 𝐴𝐵 is !, and the slope
!
of 𝐵𝐶 is − !. They are opposite
reciprocals.
D. Not enough information.
V
W
A. 4
B. 5
X
Y
Z
C. 10
D. 16
57. What is the slope of the line parallel
to the line given by the below
equation?
3𝑥 − 2𝑦 = 12
A. 2 3
B. 3 2
C. − 2 3
D. − 3 2
Fall2015
GeometryRegularSemester1Review 2015–2016
58. What is the slope of the line
perpendicular to the line given by
the below equation?
3𝑥 − 2𝑦 = 12
A. 2 3
B. 3 2
C. − 2
a
c
g
59. Angles a and d are NOT ________________.
a
b
d
c
adjacent
supplementary
complementary
a linear pair
b
d
A.
B.
C.
D.
complementary
supplementary
adjacent
vertical
h
61. Angles a & h :
A. Corresponding
B. Same-side interior
C. Alternate interior
D. Alternate exterior
62. Angles a & e :
A. Corresponding
B. Same-side interior
C. Alternate interior
D. Alternate exterior
60. Angles b and d are ________________.
a
b
d
f
e
3
D. − 3 2
A.
B.
C.
D.
For 61-64, use the diagram below to identify
the relationship between the angles.
c
63. Angles d & f :
A. Corresponding
B. Same-side interior
C. Alternate interior
D. Alternate exterior
64. Angles c & f :
A. Corresponding
B. Same-side interior
C. Alternate interior
D. Alternate exterior
Fall2015
GeometryRegularSemester1Review 2015–2016
65. Write the converse of the following
statement and give its truth value.
“If a number is divisible by 6, then it is
divisible by 2.”
69. JKLN is a square. M is the midpoint of
𝑁𝐿. Justify why ∆𝐽𝑁𝑀 ≅ ∆𝐾𝐿𝑀.
A. If a number is not divisible by 6,
then it is not divisible by 2. True.
B. If a number is divisible by 2, then it
is divisible by 6. False.
C. If a number is not divisible by 6,
then it is not divisible by 2. False.
D. If a number is divisible by 2, then it
is divisible by 6. True.
66. Felicia wants to install an island in her
kitchen. She wants to position the
island so that it is equidistant from the
vertices of a triangle formed by the
sink, the refrigerator, and the
stovetop. Which point of concurrency
should be used to position the island?
A.
B.
C.
D.
K
J
N
A.
B.
C.
D.
M
L
SSS
SAS
AAS
HL
Centroid
Incenter
Circumcenter
Median
67. Which point of concurrency is
equidistant to the sides of a triangle?
A.
B.
C.
D.
Centroid
Incenter
Circumcenter
Median
68. Which point of concurrency is the
center of gravity of a triangle?
A.
B.
C.
D.
Centroid
Incenter
Circumcenter
Median
Fall2015