Geometry Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Tell whether the ordered pair (5, –3) is a solution of the system
a. yes
.
b. no
2. Solve
Express your answer as an ordered pair.
a. ( 3, 2)
c. ( 4 , 1)
3
d. ( 8 , –3)
b. (2, 3)
3
3. Solve
. Express your answer as an ordered pair.
a. (8, –4)
b. (4, 8)
4. Name two lines in the figure.
c. (–2, 4)
d. (4, –8)
R
W
C
A
T
a. A and T
c.
b. WCR and TRA
d.
5. Draw and label a pair of opposite rays
a.
F
G
and
.
c.
H
F
G
F
G
H
b.
and
and
d.
H
H
F
G
6. Find the length of
.
B
–9
a.
–8
C
–7
= –7
–6
–5
–4
–3
–2
–1
0
1
c.
=7
b.
= –9
7. D is between C and E.
C
=
,
=
D
27
E
4x + 8
d.
=8
, and DE = 27. Find CE.
6x
a. CE = 17.5
c. CE = 105
b. CE = 78
d. CE = 57
8. The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from
Springfield to Junction City. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they
have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch?
S 55 mi X
|
R
J
360 mi
|
a. 125 mi
b. 145 mi
c. 180 mi
d. 305 mi
9. K is the midpoint of .
and
. Find JK, KL, and JL.
a. JK = 1, KL = 1, JL = 2
c. JK = 12, KL = 12, JL = 6
b. JK = 6, KL = 6, JL = 12
d. JK = 18, KL = 18, JL = 36
10. Find the measure of
. Then, classify the angle as acute, right, or obtuse.
C
D
B
O
a. m
b. m
11. m
; obtuse
; obtuse
and m
A
c. m
d. m
. Find m
.
; acute
; obtuse
I
L
K
J
a. m
b. m
c. m
d. m
12.
bisects
,m
a. m
= 22°
b. m
= 3°
13. Tell whether
and
, and m
. Find m
.
c. m
= 40°
d. m
= 20°
are only adjacent, adjacent and form a linear pair, or not adjacent.
F
1
B
A
2
3
4
G
C
14.
15.
16.
17.
a. not adjacent
b. only adjacent
c. adjacent and form a linear pair
Find the measure of the complement of
, where m
a.
c.
b.
d.
Find the measure of the supplement of
, where m
a.
c.
b.
d.
An angle measures 2 degrees more than 3 times its complement. Find the measure of its complement.
a.
c.
b.
d.
Find the perimeter and area of the figure.
6
6x
x+ 8
a. perimeter =
area =
b. perimeter =
area =
c. perimeter =
;
area =
;
d. perimeter =
;
area =
18. The rectangles on a quilt are 2 in. wide and 3 in. long. The perimeter of each rectangle is made by a pattern of
red thread. If there are 30 rectangles in the quilt, how much red thread will be needed?
a. 10 in.
c. 180 in.
b. 150 in.
d. 300 in.
;
with endpoints C(1, –6) and M(7, 5).
19. Find the coordinates of the midpoint of
a. (3, 1)
c. (4,  1 )
2
d. (4 1 , 1 )
b. (8, –1)
2
2
, A has coordinates (–6, –6), and M has coordinates (1, 2). Find the coordinates of N.
c. (2 1 , 2)
2
1
d. (8 , 9 1 )
20. M is the midpoint of
a. (8, 10)
b. (–5, –4)
2
21. Find CD and EF. Then determine if
2
.
y
5
4
C
3
D
2
E
–5
–4
–3
–2
1
–1
–1
1
2
3
4
5
x
–2
F
–3
–4
–5
a.
b.
c.
d.
,
,
,
,
,
,
,
,
22. Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4,
–2) to U(–2, 3).
a. –1.0 units
c. 0.0 units
b. 3.4 units
d. 7.8 units
23. Give an example of corresponding angles.
3 4
2 1
7 8
6
5
a.
and
c.
b.
and
d.
24. Identify the transversal and classify the angle pair
n
and
and
and
.
m
2
1
3
4
5 6
l
8
9 10
12 11
7
a. The transversal is line l. The angles are corresponding angles.
b. The transversal is line l. The angles are alternate interior angles.
c. The transversal is line n. The angles are alternate exterior angles.
d. The transversal is line m. The angles are corresponding angles.
25. Find m
.
>>
A
xº
(3x - 70)º
>>
B
a. m
b. m
26. Find m
= 40°
= 45°
.
C
c. m
d. m
= 35°
= 50°
R
>>
T
S (3x)º
V
U
(4x – 24)º
>>
a. m
=
c. m
=
b. m
=
d. m
=
27. In a swimming pool, two lanes are represented by lines l and m. If a string of flags strung across the lanes is
represented by transversal t, and x = 10, show that the lanes are parallel.
(3x + 4)º l
(4x – 6)º
m
t
a.
;
The angles are alternate interior angles and they are congruent, so the lanes are parallel by
the Alternate Interior Angles Theorem.
b.
;
The angles are alternate interior angles, and they are congruent, so the lanes are parallel by
the Converse of the Alternate Interior Angles Theorem.
c.
;
The angles are corresponding angles and they are congruent, so the lanes are parallel by
the Converse of the Corresponding Angles Postulate.
d.
;
The angles are same-side interior angles and they are supplementary, so the lanes are
parallel by the Converse of the Same-Side Interior Angles Theorem.
28. Use the slope formula to determine the slope of the line.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
A
–8
B
–10
a. 0
c.  3
2
b.  2
3
d. undefined
29. Milan starts at the bottom of a 1000-foot hill at 10:00 am and bikes to the top by 3:00 PM. Graph the line that
represents Milan’s distance up the hill at a given time. Find and interpret the slope of the line.
y
a.
Distance (ft)
1000
750
500
250
5
10
15
20
x
Time (h)
The slope is 200, so Milan traveled 200 feet per hour.
y
b.
Distance (ft)
1000
750
500
250
5
10
15
20
x
Time (h)
The slope is
, so Milan traveled
feet per hour.
y
Time (h)
c.
250
500
750
1000 x
Distance (ft)
The slope is
, so Milan traveled
feet per hour.
y
Time (h)
d.
250
500
750
1000
x
Distance (ft)
The slope is
, so Milan travels
feet per hour.
30. Use slopes to determine whether the lines are parallel, perpendicular, or neither.
a. neither
c. parallel
b. perpendicular
31. Write the equation of the line with slope 2 through the point (4, 7) in point-slope form.
a.
c.
b.
d.
32. Determine whether the lines
and
are parallel, intersect, or coincide.
a. intersect
c. parallel
b. coincide
33. Apply the transformation M to the triangle with the given vertices.
Identify and describe the transformation.
M: (x, y)
(x – 6, y + 2)
E(3, 0), F(1, –2), G(5, –4)
y
a.
y
c.
7
7
E'
E
–7
E'
F'
7
G'
x
F
E
–7
7
F'
G
–7
This is a translation 6 units left and 2 units
up.
F
G
G'
–7
This is a translation 6 units left.
x
y
b.
7
y
d.
7
E'
F'
G'
E
E
–7
7
x
–7
7
E'
F
x
F
G
G
F'
G' –7
–7
This is a translation 2 units left and 6 units
up.
This is a translation 6 units left and 2 units
down.
34. Apply the transformation M to the polygon with the given vertices.
Identify and describe the transformation.
M: (x, y)
(–x, –y)
A(–3, 6), B(–3, 1), C(1, 1), D(1, 6)
y
a.
y
c.
7
A
Z
B
Y
–7
W
7
D
A
D
C
B
C
X
Y
7
x
–7
X
W
–7
This is a rotation of 180° about the origin.
Z
–7
This is a reflection over the x-axis.
7
x
y
b.
y
d.
7
7
A
A
D
D
X
B
–7
C
B
Y
7
X
x
C
–7
7
Y
Z
W
x
Z
W
–7
–7
This is a rotation of 180° about the origin.
35. Determine whether triangles
and
This is a rotation of 90° clockwise about
the origin.
are congruent.
y
6
G
–6
E
F
P
Q
6
x
R
–6
a. The triangles are congruent because
can be mapped to
.
b. The triangles are congruent because
can be mapped to
.
c. The triangles are congruent because
can be mapped to
.
d. The triangles are congruent because
can be mapped to
.
36. Prove that the triangles with the given vertices are congruent.
A(3, 1), B(4, 5), C(2, 3)
D(–1, –3), E(–5, –4), F(–3, –2)
a. The triangles are congruent because
, followed by a reflection:
can be mapped onto
.
by a reflection:
by a rotation:
by a reflection:
by a rotation:
by a rotation:
b. The triangles are congruent because
, followed by a rotation:
can be mapped onto
.
c. The triangles are congruent because
can be mapped onto
, followed by another translation:
d. The triangles are congruent because
, followed by a reflection:
by a reflection:
by a translation:
.
can be mapped onto
.
by a rotation:
37. Tell whether the transformation appears to be a reflection. Explain.
a. Yes; the image appears to be flipped across a line.
b. No; the image does not appear to be flipped.
38. Reflect a figure with vertices
across the x-axis. Find the coordinates
of the new image.
a.
b.
c.
d.
39. Find the coordinates of the image of the point
when it is reflected across the line
.
a.
c.
b.
d.
40. Tell whether the transformation appears to be a translation. Explain.
a. Yes; all of the points have moved the same distance in the same direction.
b. No; not all of the points have moved the same distance.
41. Find the translation of the triangle along
.
v
a.
c.
b.
d.
42. Translate the triangle with vertices
along the vector
coordinates of the new image.
a.
b.
c.
d.
43. Rotate
with vertices R(4, –1), S(5, 3), and Q(3, 1) by 90° about the origin.
. Find the
y
a.
y
c.
S'
R'
S
S
Q'
Q
R'
Q
x
x
R
R
Q'
S'
y
b.
y
d.
S
S'
S
Q
Q'
Q
x
R
x
R'
R
Q'
R'
S'
44. The point
is rotated
about point
and then reflected across the line
coordinates of the image .
a.
c.
b.
d.
45. Tell whether the transformation appears to be a dilation. Explain.
. Find the
a. Yes; the figures are similar, and the image is not turned or flipped.
b. No; the figures are not similar.
46. Given the rectangle and the center of dilation P, which of the following is a dilation with a scale factor of 2?
P
a.
c.
P
P
b.
d.
P
P
47. On a sketch of a mural, 3 inches represents one foot in the mural. A door in the sketch is 2 inches wide by 5
inches high. What is the perimeter of the door in the mural expressed in inches?
a. 4 in.
c. 20 in.
b. 8 in.
d. 56 in.
48. A triangle with vertices
,
, and
is given. Which of the following is the image of the
triangle under a dilation with a scale factor of
centered at the origin?
y
12
8
4
A
–12
–8
–4
B
4
–4
–8
–12
8
C
12
x
y
a.
y
c.
12
12
8
8
C'
B'
4
A
–12
–8
B'
–4
A'
A'
4
B
A
4
8
12
x
–12
–8
–4
C
–4
B
4
–4
–8
8
12
x
C
–8
C'
–12
y
b.
–12
y
d.
12
12
C'
8
8
A'
4
A
–12
–8
–4
B'
4
B
4
A
8
12
x
–12
–8
–4
C
–4
B
4
–4
–8
C
8
A'
12
x
B'
–8
C'
–12
49.
2009_06_GE_03
–12
Transformations: Classifications of
In the diagram below, under which transformation will
a. rotation
b. dilation
50.
2009_06_GE_07
a.
b.
?
c. translation
d. glide reflection
Parallel and Perpendicular Lines
What is an equation of the line that passes through the point
equation is
be the image of
?
c.
d.
and is perpendicular to the line whose
51.
2009_06_GE_08
Transformations: Compositions of
After a composition of transformations, the coordinates
,
, and
, as shown on the set of axes below.
, and
become
,
Which composition of transformations was used?
a.
c.
b.
52.
2009_06_GE_18
d.
Solid Geometry: Lines and Planes in Space
Point P is on line m. What is the total number of planes that are perpendicular to line m and pass through
point P?
a. 1
c. 0
b. 2
d. infinite
53.
2009_06_GE_19
Midpoint
Square LMNO is shown in the diagram below.
What are the coordinates of the midpoint of diagonal
a.
c.
b.
54.
2009_06_GE_26
d.
Parallel and Perpendicular Lines
?
Which equation represents a line perpendicular to the line whose equation is
a.
c.
b.
d.
55.
2009_08_GE_01
?
Parallel Lines: Angles Involving
Based on the diagram below, which statement is true?
a.
b.
56.
2009_08_GE_02
c.
d.
Constructions
The diagram below shows the construction of the bisector of
57.
Which statement is not true?
a.
c.
b.
d.
2009_08_GE_06
.
Transformations: Classifications of
Which transformation produces a figure similar but not congruent to the original figure?
a.
c.
b.
d.
58.
2009_08_GE_08
Transformations: Compositions of
On the set of axes below, Geoff drew rectangle ABCD. He will transform the rectangle by using the
translation
and then will reflect the translated rectangle over the x-axis.
What will be the area of the rectangle after these transformations?
a. exactly 28 square units
c. greater than 28 square units
b. less than 28 square units
d. It cannot be determined from the
information given.
59.
2009_08_GE_09
Parallel and Perpendicular Lines
What is the equation of a line that is parallel to the line whose equation is
a.
c.
b.
d.
60.
2009_08_GE_10
Midpoint
The endpoints of
a.
b.
61.
2009_08_GE_17
?
are
and
. What are the coordinates of the midpoint of
c.
d.
Parallel and Perpendicular Lines
What is the slope of a line perpendicular to the line whose equation is
62.
a.
c.
b.
d.
2009_08_GE_19
2009_08_GE_27
?
Distance
If the endpoints of
a.
b. 2
63.
?
are
and
, what is the length of
c.
d. 8
?
Solid Geometry: Lines and Planes in Space
If two different lines are perpendicular to the same plane, they are
a. collinear
c. congruent
b. coplanar
d. consecutive
64. Triangle ABC has vertices
,
, and
. Under a translation, , the image point of A, is
located at
. Under this same translation, point
is located at
a.
c.
b.
d.
65. Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P
and R?
a.
b.
c.
d.
Planes P and R are skew.
Planes P and R are parallel.
Planes P and R are perpendicular.
Plane P intersects plane R but is not perpendicular to plane R.
66. The diagram below illustrates the construction of
Which statement justifies this construction?
a.
c.
b.
d.
parallel to
through point P.
67. The figure in the diagram below is a triangular prism.
Which statement must be true?
a.
c.
b.
d.
68. What is the equation of a line that passes through the point
is
?
a.
c.
b.
69. Line segment AB has endpoints
a.
b.
and is parallel to the line whose equation
d.
and
. What are the coordinates of the midpoint of
c.
d.
?
70. A polygon is transformed according to the rule:
units in which direction?
a. up
c. left
b. down
d. right
71. In the diagram below of
, D is a point on
,
. Every point of the polygon moves two
,
, and
.
The length of
could be
a. 5
c. 19
b. 12
d. 25
72. The lines
and
are
a. parallel
c. the same line
b. perpendicular
d. neither parallel nor perpendicular
73. What is the slope of a line perpendicular to the line whose equation is
?
a.
c.
b.
d.
74. In the diagram below, under which transformation is
a.
b.
the image of
?
c.
d.
75. Triangle ABC is similar to triangle DEF. The lengths of the sides of
length of the shortest side of
if its perimeter is 60?
a. 10
c. 20
b. 12.5
d. 27.5
are 5, 8, and 11. What is the
76. Square ABCD has vertices
square?
a.
b.
,
,
, and
. What is the length of a side of the
c.
d.
Numeric Response
77. Find the value of x so that
.
(6x + 5)º
m
(5x - 12)º
n
78. Under a rotation about the origin, the point
degrees, of the angle of rotation?
is mapped to the point
. What is the measure, in
Short Answer
79.
2009_06_GE_29
Medians, Altitudes, Bisectors and Midsegments
In the diagram of
below,
,
, and
formed by connecting the midpoints of the sides of
.
80.
2009_06_GE_31
Parallel and Perpendicular Lines
Find an equation of the line passing through the point
.
81.
2009_08_GE_31
. Find the perimeter of the triangle
and parallel to the line whose equation is
Parallel and Perpendicular Lines
Write an equation of the line that passes through the point
.
and is parallel to the line whose equation is
Geometry Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
A
B
B
C
B
C
C
A
B
B
C
D
A
A
A
D
B
D
C
A
A
D
A
A
C
D
B
B
A
A
D
A
A
B
C
D
A
B
B
A
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
A
A
A
B
B
C
D
A
A
B
C
A
D
B
D
C
B
A
C
B
D
A
B
A
B
A
C
B
B
D
B
D
B
C
B
B
NUMERIC RESPONSE
77. 17
78.
SHORT ANSWER
79. 20
80.
81.