Geometry Final Exam Review 2012
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
is an altitude,
, and
Z
. Find
.
A
X
W
Y
____
____
C
a. 34
c. 18
b. 32
d. 31
2. An isosceles triangle has a base 9.6 units long. If the congruent side lengths have measures to the first decimal
place, what is the shortest possible length of the sides?
a. 4.9
c. 4.7
b. 19.3
d. 9.7
3. Which segment is the shortest possible distance from point D to plane P?
D
P
R
Q
N
P
a.
b.
____
____
S
O
c.
d.
4. Find the measure of each interior angle for a regular pentagon. Round to the nearest tenth if necessary.
a. 360
c. 540
b. 108
d. 72
5. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if
necessary.
a. 2160
c. 154.3
b. 25.7
d. 360
Complete the statement about parallelogram ABCD.
A
B
G
D
____
6.
a.
b.
c.
d.
____
C
; Alternate interior angles are congruent.
; Alternate interior angles are congruent.
; Opposite angles of parallelograms are congruent.
; Opposite angles of parallelograms are congruent.
7.
a.
b.
c.
d.
; Opposite sides of parallelograms are congruent.
; Diagonals of parallelograms bisect each other.
; Opposite sides of parallelograms are congruent.
; Diagonals of parallelograms bisect each other.
Refer to parallelogram ABCD to answer to following questions.
y
B
A
K
C
x
D
____
____
8. What is the length of segment AK?
a.
b.
c.
d.
9. What is the distance between points A and C?
a.
c.
b.
d.
____ 10. Do the diagonals bisect each other? Justify your answer.
a. Yes;
and
b. Yes; The diagonals are not congruent.
c. No;
and
d. No; The diagonals are not congruent.
Determine whether the quadrilateral is a parallelogram. Justify your answer.
____ 11.
46°
134°
134°
a.
b.
c.
d.
46°
No; Opposite angles are congruent.
Yes; Consecutive angles are not congruent.
No; Consecutive angles are not congruent.
Yes; Opposite angles are congruent.
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.
____ 12.
a.
b.
c.
d.
,
,
,
; Slope Formula
Yes; The opposite sides have the same slope.
No; Opposite sides are the same length.
No; The opposite sides have the same slope.
Yes; Opposite sides are the same length.
Quadrilateral ABCD is a rectangle.
A
B
G
D
C
____ 13. If
and
a. 96
b. –6
____ 14. In rhombus TUVW, if
, find
, find
T
.
c. 24
d. 48
.
U
O
W
a. 56
b. 68
V
c. 34
d. 112
Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square.
List all that apply.
____ 15.
,
,
,
a. square; rectangle; rhombus
c. square
b. rhombus
d. rectangle
____ 16.
,
,
,
a. rhombus
c. square
b. square; rectangle; rhombus
d. rectangle
____ 17. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
M
L
36
A
J
32
B
K
a. 4
b. 34
c. 68
d. 40
____ 18. For trapezoid ABCD, E and F are midpoints of the legs. Let
Find GH.
5
A
be the median of ABFE.
B
E
F
D
C
9
a. 7
c. 4
b. 8
d. 6
____ 19. At Whitewater Junior High School, there are 360 students and 39 teachers. What is the ratio of students to
each teacher rounded to the nearest tenth?
a. 1:9.2
c. 120:13
b. 9.2:1
d. 13:120
____ 20. Use the number line below to determine the ratio of AD to EI.
A B C D E F G H
0
10
20
30
I
40
J K
50
a. 3:8
c. 3:4
b. 4:3
d. 8:3
____ 21. For a recent project, a teacher purchased 250 pieces of red construction paper and 114 pieces of blue
construction paper. What is the ratio of red to blue?
a. 57:125
c. 125:182
b. 125:57
d. 182:125
____ 22. A baseball player made six hits in nine innings. What is the ratio of hits to innings?
a. 2:3
c. 2:5
b. 3:2
d. 5:2
Solve each proportion.
____ 23.
a.
2
559
c.
559
2
b.
43
26
d.
26
43
a.  3
17
c.
7
10
b.
d.  17
3
____ 24.
10
7
____ 25. A hockey player made 9 goals in 12 games. Find the ratio of goals to games.
a. 3:4
c. 1:3
b. 4:3
d. 3:1
____ 26. A basketball player made 36 free throws in 16 games. Find the ratio of free throws to games.
a. 4:9
c. 6:4
b. 9:4
d. 9:5
Each pair of polygons is similar. Write a similarity statement, and find x, the measures of the indicated sides,
and the scale factor.
____ 27.
and
D
A
21.66
6.3
59° 5.7
46°
E
C
75°
7.6
59°
x
F
75°
46°
B
a.
b.
c.
d.
____ 28. CB and AB
;
;
;
;
;
;
;
;
;
; 3.8
;
;
; 3.8
; 3.8
D
H
7.8
82°
6.4
58°
E
28.08
G
7.2
73°
128° 3.6
F
C
73° A
128°
82°
x–2
58°
B
a.
b.
c.
d.
;
;
;
;
;
; 3.6
;
;
;
;
;
;
; 3.6
; 3.6
Identify the similar triangles. Find x.
____ 29.
D
A
6
15
F
9
x–5
C
E
B
a.
b.
c.
d.
____ 30.
;
;
;
;
D
C
12
A
40
10
E
a.
b.
c.
d.
F
x
;
;
;
;
B
Determine whether each pair of triangles is similar. Justify your answer.
D
____ 31.
A
24
9
E
8
10
C
F
30
27
B
a.
b.
c.
d.
No; sides are not proportional.
yes;
by SSS Similarity
yes;
by SSS Similarity
yes;
by SSS Similarity
a.
b.
c.
d.
yes;
by AA Similarity
yes;
by AA Similarity
yes;
by ASA Similarity
No; there is not enough information to determine similarity.
____ 32.
Find x and the measures of the indicated parts.
____ 33. AB and AC
a.
b.
____ 34. BC and AC
c.
d.
a.
b.
____ 35. BC and AC
c.
d.
a.
b.
____ 36. BD and CE
c.
d.
a.
b.
c.
d.
____ 37. Determine whether
. Justify your answer.
R
Q
S
P
T
,
a.
b.
,
c.
3
no,
yes,
,
3,
1
3
Find the perimeter of the given triangle.
d.
3
yes,
no,
3,
1
3
____ 38.
if
P
A
13
6
B
C
9
11
R
a. 18
b. 60.5
____ 39.
if
Q
c. 15.23
d. 22
perimeter of
A
Q
P
B
R
C
a. 72
b. 18
c. 108
d. 24
____ 40. Find PS if
is an altitude of
A
12
P
10
16
Q
B
D
S
R
C
a. 7.5
b. 19.2
c. 4.62
d. 19.5
____ 41. Find ST if
and
are altitudes and
S
5
12 – x
C
P
x
R
D
T
7
Q
a. 7
c. 17
b. 5
d. 19
____ 42. Find the geometric mean between each pair of numbers.
and
a. 22.5
c. 464
b. 3 5
d. 4 29
is an altitude of
____ 43. Find the measure of the
.
A
8
D
15
B
C
a. 2 30
b. 11.5
____ 44. Find x.
11
c.
23
d. 120
11
x
10
a. 6
b. 16
Determine whether
c.
146
d. 4 6
is a right triangle for the given vertices. Explain.
____ 45. Q(–6, –2), R(2, –5), S(–3, 6)
a. no; QR = 73 , QS = 73 , RS = 146 ; QR2 + QS2 RS2
b. yes; QR = 73 , QS = 73 , RS = 146 ; QR2 + QS2 = RS2
c. yes; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 = RQ2
d. no; QR = 73 , QS = 73 , RS = 146 ; RS2 + QS2 RQ2
____ 46. Q(18, 13), R(17, –3), S(–18, 12)
a. no; QR = 257 , QS = 1297 , RS = 5 58 ; QR2 + QS2 RS2
b. yes; QR = 257 , QS = 1297 , RS = 5 58 ; RS2 + QS2 = RQ2
c. yes; QR = 257 , QS = 1297 , RS = 5 58 ; QR2 + QS2 RS2
d. no; QR = 257 , QS = 1297 , RS = 5 58 ; RS2 + QS2 = RQ2
____ 47. Find x and y.
y
13.1
x°
a.
c.
b.
d.
____ 48. Find x and y.
x
60°
24
y
a.
c.
b.
d.
____ 49. Find the measure of the angle to the nearest tenth of a degree.
a. 30.9
c. 0.5135
b. 59.1
d. 27.2
____ 50. Use the figure to find the trigonometric ratio below. Express the answer as a decimal rounded to the nearest
ten-thousandth.
cos B
C
A
AC = 5 5 , CB =
D
B
5 , AD = 11, CD = 2, DB = 1
a. 2.2361
c. 0.4472
b. 0.9839
d. 0.8944
____ 51. Lynn is standing at horizontal ground level with the base of the Sears Tower in Chicago. The angle formed by
the ground and the line segment from her position to the top of the building is 15.7°. The height of the Sears
Tower is 1450 feet. Find her distance from the Sears Tower to the nearest foot.
a. 408 ft
c. 5159 ft
b. 7 ft
d. 5358 ft
____ 52. A space shuttle is one kilometer above sea level when it begins to climb at a constant angle of 3° for the next
80 ground kilometers. About how far above sea level is the space shuttle after its climb?
a. 4.2 km
c. 79.9 km
b. 5.2 km
d. 80.9 km
A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°.
____ 53. How far off the ground is the raised end of the drawbridge in its initial setting?
a. 5.23 yd
c. 685.80 yd
b. 59.77 yd
d. 688.42 yd
____ 54. During one stage of the drawbridge’s motion, the raised end is 18 yards above the ground. What is the incline
of the drawbridge to the nearest hundredth?
a. 0.005°
c. 17.46°
b. 16.70°
d. 72.54°
____ 55. While paddling a canoe up the river, Jan saw some beautiful flowers along the river bank. The canoe is 35
yards lower than the flowers. The distance from the canoe to the flowers is 225 yards. What is the angle of
elevation?
a. 8.8°
c. 81.1°
b. 8.9°
d. 81.2°
____ 56. A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are
10.2° and 8.7°. How far apart are the cars?
a. 58.6 m
c. 333.5 m
b. 392.1 m
d. 57.8 m
____ 57. Two cabins are observed by a ranger in a 60-foot tower above a park. The angles of depression are 11.6° and
9.4°. How far apart are the cabins?
a. 70.1 ft
c. 362.4 ft
b. 292.3 ft
d. 69.0 ft
____ 58. Two swimmers are observed by a lifeguard in a 30-foot tower above the water. The angles of depression are
12.7° and 14.5°. How far apart are the swimmers?
a. 16.6 ft
c. 116.0 ft
b. 133.1 ft
d. 17.1 ft
____ 59. After flying at an altitude of 600 meters, a hot air balloon starts to descend when its ground distance from the
landing pad is 10 kilometers. What is the angle of depression for this part of the flight?
a. 0.95°
c. 86.57°
b. 3.43°
d. 89.05°
____ 60. A water slide is 400 yards long with a vertical drop of 36.3 yards. Find the angle of depression of the slide.
a. 5.2°
c. 436.3°
b. 84.8°
d. 363.7°
Find each measure using the given measures of
. Round measures to the nearest tenth.
____ 61. If
47.1,
59.6, and
52.2, find
.
a. 45.8
c. 56.7
b. 0.8
d. 43.6
____ 62. David and his friends are building a fort on a triangular plot of land. They want to dig a moat around the fort.
The length of one side of the plot of land is 27 feet. If the angles at the end of this side are 45° and 75°, find
the length of the moat that will enclose the entire plot of land on which the fort is built.
a. 22.0 ft
c. 60 ft
b. 30.1 ft
d. 79.2 ft
____ 63. A playground is situated on a triangular plot of land. Two sides of the plot are 175 feet long and they meet at
an angle of 70°. For safety reasons, a fence is to be placed along the perimeter of the property. How much
fencing material is needed?
a. 110 ft
c. 375.8 ft
b. 200.8 ft
d. 550.8 ft
____ 64. Kim’s route from her front door to the mailbox, the swing set, and back to the front door forms a triangle.
Two legs of the triangle are 245 feet long and they meet at an angle of 38°. How long is the entire route?
a. 142 ft
c. 404.5 ft
b. 159.5 ft
d. 649.5 ft
____ 65. Two observation stations that are 15 miles apart located a ship at the same time. The first station indicated
that the position of the ship made an angle of 38° with the line between the stations. The second station
indicated that it made an angle of 36° with the same line. How far is the first station from the ship?
a. 9.17 mi
c. 15 mi
b. 9.6 mi
d. 18.77 mi
____ 66. In
, given the following measures, find the measure of the missing side to the nearest tenth..
,
,
a. b  6.7
c. b  14.5
b. b  394
d. b  45.3
Members of the soccer team are trying to map out some new plays before their next game. The goal is 24 feet
wide.
____ 67. Nina put a player 25 feet from one goal post and 35 feet from the other post. What is the player’s angle to
make a shot on goal?
a. 43.3
c. 91.1
b. 45.6
d. 1274
____ 68. Pedro came up with a play that would put him 35 feet from one goal post and 45 feet from the other post.
What is his angle to make a shot on goal?
a. 31.9
c. 100.8
b. 48.4
d. 180
____ 69. Sophie’s favorite play has a player standing 18 feet from one goal post and 21 feet from the other post. What
is the angle to make a shot on goal?
a. 43.4
c. 57.9
b. 46.6
d. 75.5
____ 70. Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from
each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to
Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in
the triangle.
a.
,
,
b.
,
,
c.
,
,
d.
,
,
____ 71. Tomas, Ling, and Daniel are experimenting with a giant rubber band. They each hold the rubber band to
create a triangle. The distance from Tomas to Ling is 24 inches. The distance from Ling to Daniel is 36
inches. The distance from Daniel to Tomas is 20 inches. Find the measures of the three angles in the triangle.
a.
,
,
b.
,
,
c.
,
,
d.
,
,
____ 72. Tiffany, Lori, and Mika are practicing for an egg-toss contest. The distance from Tiffany to Lori is 17 inches.
The distance from Lori to Mika is 32 inches. The distance from Mika to Tiffany is 28 inches. Find the
measures of the three angles in the triangle.
a.
,
,
b.
c.
d.
,
,
,
,
,
,
____ 73. Find the magnitude and direction of CD for the given coordinates. Round to the nearest tenth.
a. 18.4,
b. 8.9,
____ 74. Find the exact circumference of the circle.
c. 220.6,
d.
,
4 cm
3 cm
a. 7 cm
b. 5 cm
c. 10 cm
d. 4 cm
Use the diagram to find the measure of the given angle.
C
A
B
50°
D
F
E
____ 75.
a. 50
b. 60
c. 130
d. 40
a. 110
b. 120
c. 130
d. 140
____ 76.
Use the diagram to find the measure of the given angle.
P
S
(3x + 35)°
R
(4x + 15)°
Q
T
____ 77.
a. 95°
b. 20°
c. 50°
d. 85°
a. 85°
b. 20°
c. 50°
d. 95°
____ 78.
____ 79. In
,
,
= 7x,
= 5x + 12, and
B
F
A
C
D
E
Find m arc
a. 56
b. 46
____ 80. In
,
.
c. 50
d. 49
and AE = 10.
and
are diameters.
D
E
A
C
F
8
B
Find m
a. 14
b. 12
____ 81.
G
.
c. 10
d. 16
A
1
B
D
2
C
If
= 2x + 2,
a. 72
b. 19
= 9x, find
.
c. 75
d. 18
____ 82. Quadrilateral ABCD is inscribed in
such that
B
A
Z
C
D
a. 48
c. 46
and
. Find
.
b. 44
d. 42
____ 83. Find x. Assume that segments that appear tangent are tangent.
A
13
5
C
x
B
a. 9
c. 12
b. 7
d. 17
____ 84. Find x. Assume that segments that appear tangent are tangent.
K
x
12
J
L
O
3
7
H
N
M
a. 7
b. 5
c. 9
d. 3
Find the measure of the numbered angle.
____ 85.
105
3
135
a. 60
c. 80
b. 70
d. 65
60
____ 86.
6
50
a. 115
b. 125
c. 120
d. 130
4 a°
____ 87.
3 a°
4
6 a°
7 a°
a. 81
b. 90
c. 94
d. 102
2 x°
____ 88.
2 x°
7
4 x°
4 x°
a. 92
b. 95
c. 94
d. 90
____ 89.
9
a. 100
b. 180
c. 90
d. 95
____ 90.
10
220°
a. 70
b. 75
c. 80
d. 85
Find x. Assume that any segment that appears to be tangent is tangent.
____ 91.
x°
20°
a. 50
100°
c. 60
b. 40
d. 70
____ 92.
92°
x°
38°
62°
a. 65
b. 66
c. 68
d. 62
____ 93.
4x°
88°
12x°
a. 22
b. 9
c. 18
d. 11
____ 94.
158°
72°
x°
a. 47
b. 48
c. 44
d. 43
____ 95.
230°
90°
x°
a. 35
b. 20
c. 25
d. 30
Find x. Round to the nearest tenth if necessary.
____ 96.
6
x
2
3
a. 5
b. 6
c. 3
d. 4
____ 97.
2
3
7
x
a. 10.5
c. 3.2
b. 2.4
d. 3.5
____ 98.
5
x
3
4
a. 4.2
b. 3.8
c. 3.2
d. 3.7
____ 99.
10
x+ 1
x
3
a. 4
b. 5.5
c. 6
d. 5
____ 100.
9
x
x
4
a. 6
b. 6.5
c. 7
d. 7.2
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
____ 101.
x
3
6
a. 9
b. 2
c. 3
d. 8
____ 102.
x
12
8
a. 7.2
b. 4
c. 1.7
d. 3
____ 103.
6
2
4
x
a. 8
c. 3
b. 10
d. 4
____ 104.
x
2
5
10
a. 3
b. 7
c. 2
d. 4
____ 105.
x
7
4x
x+3
a. 3.3
b. 2.5
c. 3.1
d. 4.5
____ 106.
x
8.2
3.2
3.5
a. 8.5
b. 9.0
c. 9.3
d. 9.6
Geometry Review 2012
Answer Section
MULTIPLE CHOICE
1. ANS: A
If
is an altitude,
. The measures of the angles of every triangle add up to 180.
Feedback
A
B
C
D
Correct!
Which angle measures add up to 180?
Which angles must measure 90°?
Check your math.
PTS: 1
DIF: Average
REF: Lesson 5-2
OBJ: 5-2.1 Use altitudes in triangles.
NAT: NCTM GM.1 | NCTM GM.1a
TOP: Use altitudes in triangles.
KEY: Altitudes | Triangles
2. ANS: A
The sum of the lengths of any two sides must be greater than the third.
Feedback
A
B
C
D
Correct!
Would both sides have to be longer than the base?
Is the sum of the two sides longer than the base?
Is that the shortest possible length?
PTS: 1
DIF: Average
REF: Lesson 5-5
OBJ: 5-5.2 Determine the shortest distance between a point and a line.
NAT: NCTM AL.2 | NCTM AL.2b | NCTM GM.1
TOP: Determine the shortest distance between a point and a line.
KEY: Distance | Distance Between a Point and a Line
3. ANS: B
The shortest possible distance from point D to plane P is a straight line perpendicular to plane P through point
D.
Feedback
A
B
C
D
Is this line perpendicular to plane P?
Correct!
Is this line perpendicular to plane P?
What is the relationship between the shortest segment and the plane?
PTS:
OBJ:
NAT:
TOP:
KEY:
4. ANS:
1
DIF: Average
REF: Lesson 5-5
5-5.2 Determine the shortest distance between a point and a line.
NCTM AL.2 | NCTM AL.2b | NCTM GM.1
Determine the shortest distance between a point and a line.
Distance | Distance Between a Point and a Line
B
To find the size of each interior angle of a regular polygon, use the formula
.
Feedback
A
B
C
D
This is the sum of the exterior angles.
Correct!
This is the sum of all of the interior angles, not each individual angle.
This is the value of each exterior angle.
PTS:
OBJ:
NAT:
TOP:
KEY:
5. ANS:
1
DIF: Average
REF: Lesson 6-1
6-1.1 Find the sum of the measures of the interior angles of a polygon.
NCTM GM.1 | NCTM GM.1a | NCTM ME.1
Find the sum of the measures of the interior angles of a polygon.
Interior Angles | Polygons
C
To find the size of each interior angle of a regular polygon, use the formula
.
Feedback
A
B
C
D
This is the sum of all of the interior angles, not each individual angle.
This is the value of each exterior angle.
Correct!
This is the sum of the exterior angles.
PTS: 1
DIF: Average
REF: Lesson 6-1
OBJ: 6-1.1 Find the sum of the measures of the interior angles of a polygon.
NAT: NCTM GM.1 | NCTM GM.1a | NCTM ME.1
TOP: Find the sum of the measures of the interior angles of a polygon.
KEY: Interior Angles | Polygons
6. ANS: C
Locate the angle on the parallelogram. Using the properties of parallelograms, determine which angle is
congruent to that angle.
Feedback
A
B
C
D
Why are these angles congruent?
Check the angle and reason.
Correct!
This angle is not congruent to the original angle.
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.1 Recognize and apply properties of the sides and angles of parallelograms.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of the sides and angles of parallelograms.
KEY: Parallelograms | Properties of Parallelograms
7. ANS: C
Locate the indicated segment on the parallelogram. Using the properties of parallelograms, determine which
segment is congruent to that segment.
Feedback
A
B
C
D
This segment is not congruent to the original segment.
Why are these segments congruent?
Correct!
Check the segment and reason.
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.1 Recognize and apply properties of the sides and angles of parallelograms.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of the sides and angles of parallelograms.
KEY: Parallelograms | Properties of Parallelograms
8. ANS: C
Use the distance formula to determine the missing length. The distance formula is
.
Feedback
A
B
C
D
This is the length of DK.
This is the length of BD.
Correct!
This is the length of AC.
PTS: 1
DIF: Basic
REF: Lesson 6-2
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of diagonals of parallelograms.
KEY: Parallelograms | Properties of Parallelograms | Diagonals
9. ANS: D
Use the distance formula to determine the missing length. The distance formula is
.
Feedback
A
B
C
D
This is the length of DK.
This is the length of BD.
This is the length of AK.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 6-2
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of diagonals of parallelograms.
KEY: Parallelograms | Properties of Parallelograms | Diagonals
10. ANS: A
Use the distance formula to determine the lengths of the segments. The distance formula is
. In order for the diagonals to be bisected, each segment of the diagonal should
be congruent.
Feedback
A
Correct!
B
C
D
Do the diagonals need to be congruent?
If the diagonals bisect each other, these segments should be congruent.
Check the measurements of the segments.
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.2 Recognize and apply properties of diagonals of parallelograms.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of diagonals of parallelograms.
KEY: Parallelograms | Properties of Parallelograms | Diagonals
11. ANS: D
Using the properties of parallelograms, study the quadrilateral. If it satisfies the properties, it is a
parallelogram.
Feedback
A
B
C
D
This is a reason why quadrilaterals are parallelograms.
Do consecutive angles have to be congruent to form a parallelogram?
Do consecutive angles need to be congruent?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 6-3
OBJ: 6-3.1 Recognize the conditions that ensure a quadrilateral is a parallelogram.
NAT: NCTM GM.1c | NCTM GM.2 | NCTM GM.2b
STA: 4.2.12 A.3
TOP: Recognize the conditions that ensure a quadrilateral is a parallelogram.
KEY: Quadrilaterals | Parallelograms | Determining a Parallelogram
12. ANS: A
Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent,
the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a
parallelogram.
Feedback
A
B
C
D
Correct!
Which method was used to solve the problem?
This is a valid reason for the quadrilateral to be a parallelogram.
Did you use the method in the directions?
PTS: 1
DIF: Average
REF: Lesson 6-3
OBJ: 6-3.2 Prove that a set of points forms a parallelogram in the coordinate plane.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Prove that a set of points forms a parallelogram in the coordinate plane.
KEY: Parallelograms | Determining a Parallelogram
13. ANS: A
The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable.
Use the variable’s value to solve for the diagonal length.
Feedback
A
B
C
D
Correct!
This is the value of the variable not the length of the diagonal.
Multiply, not divide, by two to find the length of the diagonal.
This is not the length of the entire diagonal.
PTS: 1
DIF: Average
REF: Lesson 6-4
OBJ: 6-4.1 Recognize and apply properties of rectangles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply properties of rectangles.
KEY: Rectangles | Properties of Rectangles
14. ANS: A
The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.
Feedback
A
B
C
D
Correct!
Doubling the given angle does not give the answer.
This is the size of the given angle.
Which angle is asked for?
PTS: 1
DIF: Basic
REF: Lesson 6-5
OBJ: 6-5.1 Recognize and apply properties of rhombi.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply the properties of rhombi.
KEY: Rhombi | Properties of Rhombi
15. ANS: A
Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is
either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals
are congruent and perpendicular, the quadrilateral is a square.
Feedback
A
B
C
D
Correct!
Are the angles congruent?
Remember to list all that apply.
Are the sides congruent?
PTS: 1
DIF: Average
REF: Lesson 6-5
OBJ: 6-5.2 Recognize and apply the properties of squares.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply the properties of squares.
KEY: Squares | Properties of Squares
16. ANS: B
Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is
either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals
are congruent and perpendicular, the quadrilateral is a square.
Feedback
A
B
C
D
Are the angles congruent?
Correct!
Remember to list all that apply.
Are the sides congruent?
PTS:
OBJ:
STA:
KEY:
17. ANS:
1
DIF: Average
REF: Lesson 6-5
6-5.2 Recognize and apply the properties of squares.
NAT: NCTM GM.1 | NCTM GM.1a
4.2.12 A.3
TOP: Recognize and apply the properties of squares.
Squares | Properties of Squares
D
To find the other base, substitute the given values into the formula,
..
Feedback
A
B
C
D
Do not subtract the base from the median.
AB is the median not a base.
Do not add the median and base.
Correct!
PTS: 1
DIF: Average
REF: Lesson 6-6
OBJ: 6-6.1 Recognize and apply the properties of trapezoids.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Recognize and apply the properties of trapezoids.
KEY: Trapezoids | Properties of Trapezoids
18. ANS: D
To find the median, find the sum of the bases and then divide by two.
Feedback
A
B
C
D
This is the median of ABCD.
Where is the median of ABFE located?
How do you find the median of a trapezoid?
Correct!
PTS: 1
DIF: Average
REF: Lesson 6-6
OBJ: 6-6.2 Solve problems involving the medians of trapezoids.
NAT: NCTM GM.2 | NCTM GM.2a
STA: 4.2.12 A.3
TOP: Solve problems involving the medians of trapezoids.
KEY: Trapezoids | Medians | Medians of Trapezoids
19. ANS: B
To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest
tenth.
Feedback
A
B
C
D
This is the ratio of teacher to students.
Correct!
The question asks for the unit ratio.
This is the ratio of teachers to students.
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
20. ANS: C
Find the length of AD. Then find the length of EI. Write the ratio in simplest form.
Feedback
A
B
C
D
What is the length of EI?
This is the ratio of EI to AD.
Correct!
What is the length of EI?
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
21. ANS: B
Find the number of pieces of red construction paper. Find the number of pieces of blue construction paper.
Simplify the ratio.
Feedback
A
B
C
D
This is the ratio of blue to red construction paper.
Correct!
This is the ratio of red to all construction paper.
This is the ratio of all construction paper to red.
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
22. ANS: A
How many hits does the player have? How many innings did the player play? Simplify the ratio.
Feedback
A
B
C
D
Correct!
This is the ratio of innings to hits.
Do not add the number of innings and hits.
How many innings are in the game?
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
23. ANS: D
Find the cross products. Multiply. Divide each side by the coefficient of the variable.
Feedback
A
B
C
D
Remember to cross multiply.
Reverse the numerator and denominator.
Remember to cross multiply.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.2 Use properties of proportions.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Use properties of proportions.
KEY: Proportions
24. ANS: D
Find the cross products. Multiply. Divide each side by the coefficient of the variable.
Feedback
A
B
C
D
Reverse the numerator and denominator.
Check your cross multiplication.
The left side of the proportion cannot be reduced before cross multiplying.
Correct!
PTS:
NAT:
KEY:
25. ANS:
1
DIF: Average
NCTM GM.1 | NCTM GM.1b
Proportions
A
REF: Lesson 7-1
OBJ: 7-1.2 Use properties of proportions.
TOP: Use properties of proportions.
How many goals are scored? How many games are played? Simplify the results.
Feedback
A
B
C
D
Correct!
This is the ratio of games to goals.
Do not subtract the number of goals from the number of games.
Do not subtract the number of goals from the number of games.
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
26. ANS: B
How many free throws were scored? How many games are played? The ratio should be written in simplest
form.
Feedback
A
B
C
D
This is the ratio of games to free throws.
Correct!
Do not take the square root of the numbers.
Do not subtract the number of games from the number of free throws.
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
NAT: NCTM NO.3 | NCTM NO.3a
TOP: Write ratios. KEY: Ratios
27. ANS: C
Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing
information.
Feedback
A
B
C
D
Check the similarity statement.
Remember to include all of the information.
Correct!
Check the similarity statement.
PTS: 1
DIF: Average
REF: Lesson 7-2
OBJ: 7-2.2 Solve problems involving scale factors.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Solve problems involving scale factors.
KEY: Scale Factors | Solve Problems
28. ANS: C
Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing
information.
Feedback
A
B
C
D
Remember to include all of the information.
Check the similarity statement.
Correct!
Check the similarity statement.
PTS:
OBJ:
TOP:
29. ANS:
1
DIF: Average
REF: Lesson 7-2
7-2.2 Solve problems involving scale factors.
Solve problems involving scale factors.
A
NAT: NCTM GM.1 | NCTM GM.1b
KEY: Scale Factors | Solve Problems
The ratio of corresponding sides is 2:3.
Feedback
A
B
C
D
Correct!
Check your cross multiplication.
Check the similarity statement.
Check the similarity statement.
PTS:
NAT:
KEY:
30. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1b
Similar Triangles
B
REF: Lesson 7-3
STA: 4.2.12 E.1
OBJ: 7-3.1 Identify similar triangles.
TOP: Identify similar triangles.
Feedback
A
B
C
D
Is AC the same length as EF?
Correct!
Check the ratio of the corresponding sides.
Check the similarity statement.
PTS: 1
DIF: Basic
REF: Lesson 7-3
OBJ: 7-3.1 Identify similar triangles.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 E.1
TOP: Identify similar triangles.
KEY: Similar Triangles
31. ANS: C
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional. The ratio of the corresponding sides is 1:3.
Feedback
A
B
C
D
Are the sides proportional?
Check the similarity statement.
Correct!
Check the similarity statement.
PTS:
NAT:
KEY:
32. ANS:
1
DIF: Basic
NCTM GM.1 | NCTM GM.1b
Similar Triangles
A
So,
REF: Lesson 7-3
STA: 4.2.12 E.1
OBJ: 7-3.1 Identify similar triangles.
TOP: Identify similar triangles.
.
Feedback
A
B
C
D
Correct!
Check the similarity statement.
Is there an ASA similarity?
The triangles are similar.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.1 Identify similar triangles.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 E.1
TOP: Identify similar triangles.
KEY: Similar Triangles
33. ANS: B
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Check the variables.
Correct!
Can the lengths of a triangle be negative?
Check the values of each side.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 E.1
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
34. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Which side of the triangle is BC?
Check the ratio.
What is the length of AC?
PTS:
OBJ:
STA:
KEY:
35. ANS:
1
DIF: Average
REF: Lesson 7-3
7-3.2 Use similar triangles to solve problems.
NAT: NCTM GM.1 | NCTM GM.1b
4.2.12 E.1
TOP: Use similar triangles to solve problems.
Similar Triangles | Solve Problems
A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
What is the length of AC?
Check the ratios.
What is the value of x?
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 E.1
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
36. ANS: D
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Check your work.
Check your ratios.
Check your substitution.
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 E.1
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
37. ANS: C
Determine the ratio for both sides of the triangle. If the ratios are congruent, then the segments are parallel.
Feedback
A
B
C
D
If the ratios are congruent, then the segments are parallel.
Check your ratios.
Correct!
Check your ratios.
PTS: 1
DIF: Average
REF: Lesson 7-4
OBJ: 7-4.1 Use proportional parts of triangles.
NAT: NCTM GM.4 | NCTM GM.4a
TOP: Use proportional parts of triangles. KEY: Proportional Parts | Triangles
38. ANS: A
If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.
Feedback
A
B
C
D
Correct!
Interchange the numerator and the denominator on either side of the proportion.
Use the correct proportion.
Check the proportion again.
PTS: 1
DIF: Basic
REF: Lesson 7-5
OBJ: 7-5.1 Recognize and use proportional relationships of corresponding perimeters of similar triangles.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Recognize and use proportional relationships of corresponding perimeters of similar triangles.
KEY: Proportional Relationships | Triangles
39. ANS: A
If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.
Feedback
A
B
C
D
Correct!
Interchange the numerator and the denominator on either side of the proportion.
If two triangles are similar, then the perimeters are proportional to the measures of the
corresponding sides.
Check your proportion again.
PTS: 1
DIF: Basic
REF: Lesson 7-5
OBJ: 7-5.1 Recognize and use proportional relationships of corresponding perimeters of similar triangles.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Recognize and use proportional relationships of corresponding perimeters of similar triangles.
KEY: Proportional Relationships | Triangles
40. ANS: A
If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures
of the corresponding sides.
Feedback
A
B
C
D
Correct!
Interchange the numerator and the denominator on either side of the proportion.
Use the correct proportion.
If two triangles are similar, then the measures of the corresponding altitudes are
proportional to the measures of the corresponding sides.
PTS: 1
DIF: Basic
REF: Lesson 7-5
OBJ: 7-5.2 Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and
medians of similar triangles.
NAT: NCTM GM.3
TOP: Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians
of similar triangles. KEY: Proportional Relationships | Triangles
41. ANS: A
If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures
of the corresponding sides.
Feedback
A
B
C
D
Correct!
The length of QC must be less than 7.
Check your calculations again.
The value of x cannot be negative.
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.2 Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and
medians of similar triangles.
NAT: NCTM GM.3
TOP: Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians
of similar triangles. KEY: Proportional Relationships | Triangles
42. ANS: D
Find the product of the given numbers. Find the square root of the product.
Feedback
A
B
C
D
This is the arithmetic mean not geometric mean.
How do you find the geometric mean?
Remember to take the square root of the product.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 8-1
OBJ: 8-1.1 Find the geometric mean between two numbers.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Find the geometric mean between two numbers.
KEY: Geometric Mean
43. ANS: A
The altitude is the geometric mean between the measures of the two segments of the hypotenuse.
Feedback
A
B
C
D
Correct!
This is the arithmetic mean not geometric mean.
How do you find the geometric mean?
Remember to take the square root of the product.
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.2 Solve problems involving relationships between parts of a right triangle and the altitude
hypotenuse.
NAT: NCTM GM.1 | NCTM GM.1b
TOP: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse.
KEY: Triangles | Altitudes | Hypotenuse
44. ANS: D
Divide the large triangle into two right triangles. Which side is the hypotenuse? Which sides are the legs?
Substitute the values into the Pythagorean Theorem to solve for the missing variable.
Feedback
A
B
C
D
Remember to square the numbers.
Which side is the hypotenuse?
Which side is the hypotenuse?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 8-2
OBJ: 8-2.1 Use the Pythagorean Theorem.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 A.1 | 4.2.12 E.1
TOP: Use the Pythagorean Theorem.
KEY: Pythagorean Theorem
45. ANS: B
Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter
sides is equal to the square of the third side, the triangle is a right triangle.
Feedback
A
B
C
D
What is the converse of the Pythagorean Theorem?
Correct!
Check the Pythagorean Theorem.
Check the Pythagorean Theorem.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Use the converse of the Pythagorean Theorem.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 A.1 | 4.2.12 E.1
TOP: Use the converse of the Pythagorean Theorem.
KEY: Converse of Pythagorean Theorem
46. ANS: A
Use the distance formula to determine the lengths of the sides. If the sum of the squares of the two shorter
sides is equal to the square of the third side, the triangle is a right triangle.
Feedback
A
B
C
D
Correct!
Check the Pythagorean Theorem.
What is the converse of the Pythagorean Theorem?
Check the Pythagorean Theorem.
PTS: 1
DIF: Average
REF: Lesson 8-2
OBJ: 8-2.2 Use the converse of the Pythagorean Theorem.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 A.1 | 4.2.12 E.1
TOP: Use the converse of the Pythagorean Theorem.
KEY: Converse of Pythagorean Theorem
47. ANS: D
The length of the hypotenuse is equal to the length of a leg times
. The diagonal of a square bisects the
angle.
Feedback
A
B
C
D
Multiply by the square root of two to find the length of the hypotenuse.
Check the length of the hypotenuse and the size of the angle.
The diagonal of a square bisects the angle.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 8-3
OBJ: 8-3.1 Use properties of 45°-45°-90° triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 A.3
TOP: Use properties of 45°-45°-90° triangles.
KEY: Triangles | 45-45-90 Triangles
48. ANS: D
The shorter leg is half the length of the hypotenuse. The longer leg is
times the length of the shorter leg.
Feedback
A
B
C
D
How do you find the length of the side opposite the 60° angle?
Switch the x and y values.
How do you find the length of the side opposite the 30° angle?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 8-3
OBJ: 8-3.2 Use properties of 30°-60°-90° triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 A.3
TOP: Use properties of 30°-60°-90° triangles.
KEY: Triangles | 30-60-90 Triangles
49. ANS: B
In trigonometry, you can find the measure of an angle by using the inverse of sine, cosine, or tangent.
Feedback
A
Which trigonometric ratio should be used?
B
C
D
Correct!
This is the ratio not the angle.
Which trigonometric ratio should be used?
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.1 Find trigonometric ratios using right triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Find trigonometric ratios using right triangles.
KEY: Trigonometric Ratios | Right Triangles
50. ANS: C
Determine the ratio associated with the given trigonometric term. Divide the numerator by the denominator.
Feedback
A
B
C
D
Check the setup of the ratio.
Which trigonometric ratio are you asked to find?
Correct!
Which trigonometric ratio are you asked to find?
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.1 Find trigonometric ratios using right triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Find trigonometric ratios using right triangles.
KEY: Trigonometric Ratios | Right Triangles
51. ANS: C
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Check the trigonometric ratio.
Which trigonometric ratio should be used?
Correct!
Which trigonometric ratio should be used?
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.2 Solve problems using trigonometric ratios.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Solve problems using trigonometric ratios.
KEY: Trigonometric Ratios | Solve Problems
52. ANS: B
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Remember to include the initial height of one kilometer.
Correct!
Which trigonometric ratio should be used?
Which trigonometric ratio should be used?
PTS:
OBJ:
STA:
KEY:
1
DIF: Average
REF: Lesson 8-4
8-4.2 Solve problems using trigonometric ratios.
NAT: NCTM GM.1 | NCTM GM.1d
4.2.12 E.1
TOP: Solve problems using trigonometric ratios.
Trigonometric Ratios | Solve Problems
53. ANS: A
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Correct!
Do not use the cosine ratio.
What is the sine ratio?
What is the sine ratio?
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.1 Solve problems involving angles of elevation.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of elevation.
KEY: Angle of Elevation
54. ANS: C
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Did you use the inverse sine to solve.
Do not use the tangent ratio.
Correct!
Do not use the cosine ratio.
PTS: 1
DIF: Basic
REF: Lesson 8-5
OBJ: 8-5.1 Solve problems involving angles of elevation.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of elevation.
KEY: Angle of Elevation
55. ANS: B
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Do not use the tangent ratio.
Correct!
Do not use the cosine ratio.
Do not use the tangent ratio.
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.1 Solve problems involving angles of elevation.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of elevation.
KEY: Angle of Elevation
56. ANS: A
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Correct!
This is the horizontal distance from one car to the helicopter.
This is the horizontal distance from one car to the helicopter.
Which trigonometric ratio did you use?
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of depression.
KEY: Angle of Depression
57. ANS: A
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Correct!
This is the horizontal distance from the tower to a cabin.
This is the horizontal distance from the tower to a cabin.
Which trigonometric ratio did you use?
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of depression.
KEY: Angle of Depression
58. ANS: D
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Which trigonometric ratio did you use?
This is the ground distance from one swimmer to the tower.
This is the ground distance from one swimmer to the tower.
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of depression.
KEY: Angle of Depression
59. ANS: B
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
C
D
Remember to convert kilometers to meters.
Correct!
Remember to convert kilometers to meters.
Check the ratio.
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of depression.
KEY: Angle of Depression
60. ANS: A
Draw a picture of the situation. Determine which trigonometric ratio should be used to solve. Substitute the
numbers given. Solve for the answer.
Feedback
A
B
Correct!
Do not use the cosine ratio.
C
D
Do not add together the numbers given.
Do not subtract the numbers given.
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
NAT: NCTM GM.1 | NCTM GM.1d
TOP: Solve problems involving angles of depression.
KEY: Angle of Depression
61. ANS: C
Substitute the given values into the Law of Sines. Cross multiply. Divide each side by the length of side l.
Feedback
A
B
C
D
Check the Law of Sines to determine the setup of the ratios.
Remember to take the inverse of sine to solve for the angle.
Correct!
Remember to divide both sides by the length of side l.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.1 Use the Law of Sines to solve triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Use the Law of Sines to solve triangles.
KEY: Law of Sines | Solve Triangles
62. ANS: D
Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the
missing sides. Find the perimeter.
Feedback
A
B
C
D
This is only one side of the plot of land.
This is only one side of the plot of land.
This is the size of the missing angle.
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.2 Solve problems by using the Law of Sines.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Sines.
KEY: Law of Sines | Solve Problems
63. ANS: D
Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the
missing side. Find the perimeter.
Feedback
A
B
C
D
This is the sum of the other two angles of the triangle.
This is the length of one side of the triangle.
Remember to include all three sides.
Correct!
PTS:
OBJ:
STA:
KEY:
64. ANS:
1
DIF: Average
REF: Lesson 8-6
8-6.2 Solve problems by using the Law of Sines.
NAT: NCTM GM.1 | NCTM GM.1d
4.2.12 E.1
TOP: Solve problems by using the Law of Sines.
Law of Sines | Solve Problems
D
Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the
missing side. Find the perimeter.
Feedback
A
B
C
D
This is the sum of the other two angles of the triangle.
This is the length of one side of the triangle.
Remember to include all three sides.
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.2 Solve problems by using the Law of Sines.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Sines.
KEY: Law of Sines | Solve Problems
65. ANS: A
Draw a picture of the situation. Use the Law of Sines to solve. Substitute the numbers given. Solve for the
requested side.
Feedback
A
B
C
D
Correct!
This is the distance from the second station.
This is the distance between stations.
Do not combine the distances.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.2 Solve problems by using the Law of Sines.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Sines.
KEY: Law of Sines | Solve Problems
66. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the square root of both sides.
Feedback
A
B
C
D
Correct!
Check the equation for the Law of Cosines.
Should sine or cosine be used to solve the problem?
Remember to find the square root of this number.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.3 Use the Law of Cosines to solve triangles.
NAT: NCTM GM.1 | NCTM GM.1d
STA: 4.2.12 E.1
TOP: Use the Law of Cosines to solve triangles.
KEY: Law of Cosines | Solve Triangles
67. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Correct!
The goal is opposite the angle.
The goal is opposite the angle.
A few more steps must be completed to solve the problem.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
68. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Correct!
The goal is opposite the angle.
The goal is opposite the angle.
There are a total of 180 degrees in a triangle not just one angle.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
69. ANS: D
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Remember to use cosine not sine to solve.
The goal is opposite the given angle.
The goal is opposite the given angle.
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
70. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Correct!
Which angle goes with each vertex?
Which angle goes with each vertex?
The triangle is not equilateral.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
71. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Correct!
Which angle goes with each vertex?
Which angle goes with each vertex?
The triangle is not equilateral.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
72. ANS: A
Substitute the given values into the Law of Cosines. Simplify the equation. Find the measure of the stated
angle by using inverse cosine.
Feedback
A
B
C
D
Correct!
Which angle goes with each vertex?
Which angle goes with each vertex?
The triangle is not equilateral.
PTS: 1
DIF: Average
REF: Lesson 8-6
OBJ: 8-6.4 Solve problems by using the Law of Cosines.
NAT: NCTM PS.1 | NCTM PS.2 | NCTM PS.3
STA: 4.2.12 E.1
TOP: Solve problems by using the Law of Cosines.
KEY: Law of Cosines | Solve Problems
73. ANS: A
To find the magnitude, find the distance between the given points. To find the direction, use the tangent ratio.
Feedback
A
B
C
D
Correct!
How do you find magnitude?
Which is the magnitude?
How do you find magnitude?
PTS: 1
DIF: Average
REF: Lesson 8-7
OBJ: 8-7.1 Find magnitude and direction of vectors.
NAT: NCTM GM.3 | NCTM GM.3a
STA: 4.2.12 C.2
TOP: Find magnitudes and directions of vectors.
KEY: Vectors
74. ANS: B
The circumference formula is diameter  . The diameter shown also happens to be the hypotenuse of the
right triangle inscribed in the circle, so it can be found by using the Pythagorean Theorem.
Feedback
A
B
C
D
Use the Pythagorean Theorem.
Correct!
How did you find the diameter?
Use the Pythagorean Theorem.
PTS: 1
DIF: Average
REF: Lesson 10-1
OBJ:
NAT:
TOP:
75. ANS:
10-1.2 Solve problems involving the circumference of a circle.
NCTM GM.1 | NCTM GM.1a | NCTM ME.2
STA: 4.2.12 A.3
Solve problems involving the circumference of a circle.
KEY: Circles | Circumference
A
is a vertical angle with
, so they are congruent.
Feedback
A
B
C
D
Correct!
Remember vertical angles.
How are vertical angles related?
Remember vertical angles.
PTS:
OBJ:
NAT:
TOP:
KEY:
76. ANS:
1
DIF: Basic
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
NCTM ME.2
STA: 4.2.12 A.3
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
C
is equal to the sum of
and
..
Feedback
A
B
C
D
Add the two angles that make up this angle.
Add the two angles that make up this angle.
Correct!
What two angles did you add together?
PTS:
OBJ:
NAT:
TOP:
KEY:
77. ANS:
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
NCTM ME.2
STA: 4.2.12 A.3
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
A
and
are vertical angles and are therefore congruent. So, set the two expressions equal and solve
for x.
Feedback
A
B
C
D
Correct!
That's the answer for x, you need the measure of
Did you use vertical angles?
How are vertical angles related?
.
PTS:
OBJ:
NAT:
TOP:
KEY:
78. ANS:
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
NCTM ME.2
STA: 4.2.12 A.3
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
A
and
are a linear pair and are therefore supplementary. First find
.
and
vertical angles and are therefore congruent. So, set the two expressions equal and solve for x.
are
Feedback
A
B
C
D
Correct!
That's the answer for x, you need the measure of
Did you use vertical angles?
Did you use a linear pair?
.
PTS:
OBJ:
NAT:
TOP:
KEY:
79. ANS:
Since
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
NCTM ME.2
STA: 4.2.12 A.3
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
D
is a diameter,
. Solve the equation, then substitute the value of x to find
. Since
and
are vertical angles, they are congruent. Additionally, use the fact that
m arc DC =
.
Feedback
A
B
C
D
Did you make use of vertical angles?
Did you solve for x?
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-2 OBJ: 10-2.2 Find arc length.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 4.2.12 A.3
TOP: Find arc length.
KEY: Arcs | Arc Length
80. ANS: B
Since
,
and
form a right triangle, you can use the Pythagorean Theorem to find
. Since
is a
segment that passes through the center of the circle and is perpendicular to chord
, it also bisects
. That
means
.
Feedback
A
B
C
D
You need to double the length of EF.
Correct!
The hypotenuse is not the solution.
Use the other leg of triangle AFE.
PTS: 1
DIF: Average
REF: Lesson 10-3
OBJ: 10-3.1 Recognize and use relationships between arcs and chords.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Recognize and use relationships between arcs and chords.
KEY: Arcs | Chords | Diameters
81. ANS: D
m
= 90 since it is inscribed in a semicircle. Since the sum of the angles in any triangle is 180°,
+
= 90. Substitute the given values for
and
into that equation. Then substitute the value
found for x into the expression for .
Feedback
A
B
C
D
You are looking for .
+
= 90.
Did you find the value of x?
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-4
OBJ: 10-4.1 Find measures of inscribed angles.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of inscribed angles. KEY: Inscribed Angles | Measure of Inscribed Angles
82. ANS: D
First note that m arc BC =
because a central angle of a circle is always congruent to its intercepted
arc. Secondly,
is one-half m arc BC, as the measure of an inscribed angle is half the measure of its
intercepted arc. Since
,
because alternate interior angles are congruent. So
.
Feedback
A
B
C
D
Look for alternate interior angles.
Look for alternate interior angles.
Did you find the measure of
?.
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-4
OBJ: 10-4.2 Find measures of angles of inscribed polygons.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Find measures of angles of inscribed polygons.
KEY: Inscribed Polygons | Measure of Inscribed Angles
83. ANS: C
The triangle shown is a right triangle since the tangent segment, CB, intersects a radius, AB, which always
results in a right angle. So to solve for x, use the Pythagorean Theorem.
Feedback
A
B
C
D
Did you use the Pythagorean Theorem?
Use the Pythagorean Theorem.
Correct!
Is the triangle a right triangle?
PTS: 1
DIF: Average
REF: Lesson 10-5 OBJ: 10-5.1 Use properties of tangents.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 4.2.12 A.3
TOP: Use properties of tangents.
KEY: Tangents
84. ANS: B
Recall that two tangents from the same external point are congruent. So, for example,
and
. Those two equalities, plus the fact that
allows us to make the equality
. Substitute the appropriate values into that equation and solve for x.
Feedback
A
B
C
D
Are two tangents to a circle from the same external point congruent?
Correct!
The
and
.
The
and
.
PTS: 1
DIF: Average
REF: Lesson 10-5
OBJ: 10-5.2 Solve problems involving circumscribed polygons.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Solve problems involving circumscribed polygons.
KEY: Circumscribed Polygons
85. ANS: A
When two secants intersect in the interior of a circle, then the measure of an angle formed by this intersection
is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. In this
diagram, the measures of the intercepted arcs for
are not given, but they must have a sum of 120° since the
arcs shown have a sum of 240 (360 – 240 = 120).
Feedback
A
B
C
D
Correct!
Did you use the correct arcs?
Add the intercepted arcs and divide by 2.
Did you divide correctly?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
86. ANS: B
When two secants intersect in the interior of a circle, then the measure of an angle formed by this intersection
is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. In this
diagram, the measures of the intercepted arcs for
are not given, but they have a sum of 250 since the arcs
shown have a sum of 110 (360 – 110 = 250).
Feedback
A
B
C
D
Add the intercepted arcs and divide by 2.
Correct!
Did you divide correctly?
How do you find the measures of the other two arcs?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
87. ANS: A
When two secants intersect in the interior of a circle, then the measure of an angle formed by this intersection
is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. In this
diagram the measures of the intercepted arcs for
are not given. However, the full circle measures 360°, so
3a° + 4a° +6a° +7a° = 360°. Solving this equation, a = 18. So the intercepted arcs for
are 54° and 108°.
Feedback
A
B
C
D
Correct!
What is the sum of the measures of the arcs intercepted by
Add the intercepted arcs and divide by 2.
Did you find the value of a?
and its vertical angle?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
88. ANS: D
When two secants intersect in the interior of a circle, then the measure of an angle formed by this intersection
is equal to one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. In this
diagram the measures of the intercepted arcs for
are not given. However, the full circle measures 360°, so
2x° + 2x° +4x° +4x° = 360°. Solving this equation, x = 30. So the intercepted arcs for
are 60° and 120°.
Feedback
A
B
C
D
What are the measures of the intercepted arcs of
Did you find the value of x?.
Add the intercepted arcs and divide by 2.
Correct!
and its vertical angle?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
89. ANS: C
When a secant intersects a tangent at the point of tangency, then the measure of the angle formed is one-half
the measure of the intercepted arc. In this diagram, the measure of the intercepted arc for
is 180 because
the chord is also a diameter of the circle.
Feedback
A
B
C
D
Find half the measure of the intercepted arc.
Should you have divided by two?
Correct!
Find half the measure of the intercepted arc.
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
90. ANS: A
When a secant intersects a tangent at the point of tangency, then the measure of the angle formed is one-half
the measure of the intercepted arc. In this diagram, the measure of the intercepted arc for
is 140 since
360 – 220 = 140.
Feedback
A
B
C
D
Correct!
Find half the measure of the intercepted arc.
How are the measures of the angle and the intercepted arc related?
Find half the measure of the intercepted arc.
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
91. ANS: B
When two secants intersect in the exterior of a circle, then the measure of the angle formed is equal to onehalf the positive difference of the measures of the intercepted arcs.
Feedback
A
B
C
D
Did you subtract carefully?
Correct!
Use subtraction, not addition.
Did you find one-half of the positive difference?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
92. ANS: A
When two secants intersect in the exterior of a circle, then the measure of the angle formed is equal to onehalf the positive difference of the measures of the intercepted arcs.
Feedback
A
B
C
D
Correct!
What is the measure of the other intercepted arc?
Check your subtraction.
Did you find the positive difference of the measures of the intercepted arcs?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
93. ANS: A
When a secant and tangent intersect in the exterior of a circle, then the measure of the angle formed is equal
to one-half the positive difference of the measures of the intercepted arcs.
Feedback
A
B
C
D
Correct!
Did you subtract carefully?
What is the relationship between the angle and the intercepted arcs?
Check your subtraction.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
REF: Lesson 10-6
10-6.2 Find measures of angles formed by lines intersecting outside the circle.
NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
Find measures of angles formed by lines intersecting outside the circle.
Measure of Angles | Circles
94. ANS: D
When a secant and tangent intersect in the exterior of a circle, then the measure of the angle formed is equal
to one-half the positive difference of the measures of the intercepted arcs.
Feedback
A
B
C
D
Did you subtract carefully?
Check your subtraction.
Were you careful with subtraction?
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
95. ANS: C
When a secant and tangent intersect in the exterior of a circle, then the measure of the angle formed is equal
to one-half the positive difference of the measures of the intercepted arcs.
Feedback
A
B
C
D
Check your subtraction.
Did you subtract carefully?
Correct.
Check your subtraction.
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
96. ANS: D
The products of the segments for each intersecting chord are equal.
Feedback
A
B
C
D
Use multiplication, not addition.
Multiply the segments and set them equal to each other.
Multiply the segments and set them equal to each other.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 10-7
OBJ: 10-7.1 Find measures of segments that intersect in the interior of a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
97. ANS: A
The products of the segments for each intersecting chord are equal.
Feedback
A
B
Correct!
Multiply the segments and set them equal to each other.
C
D
Multiply the segments and set them equal to each other.
Multiply the segments and set them equal to each other.
PTS: 1
DIF: Basic
REF: Lesson 10-7
OBJ: 10-7.1 Find measures of segments that intersect in the interior of a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
98. ANS: B
The products of the segments for each intersecting chord are equal.
Feedback
A
B
C
D
Multiply the segments and set them equal to each other.
Correct!
Multiply the segments and set them equal to each other.
Multiply the segments and set them equal to each other.
PTS: 1
DIF: Basic
REF: Lesson 10-7
OBJ: 10-7.1 Find measures of segments that intersect in the interior of a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
99. ANS: D
The products of the segments for each intersecting chord are equal.
Feedback
A
B
C
D
Did you factor correctly?
Multiply the segments and set them equal to each other.
Use multiplication, not addition.
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.1 Find measures of segments that intersect in the interior of a circle.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
100. ANS: A
The products of the segments for each intersecting chord are equal.
Feedback
A
B
C
D
Correct!
Use multiplication, not addition.
Multiply the segments and set them equal to each other.
Multiply the segments and set them equal to each other.
PTS:
OBJ:
NAT:
TOP:
1
DIF: Average
REF: Lesson 10-7
10-7.1 Find measures of segments that intersect in the interior of a circle.
NCTM GM.1 | NCTM GM.1b | NCTM ME.2
STA: 4.2.12 A.3
Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
101. ANS: A
When a secant segment and a tangent segment intersect in the exterior of a circle, set the product of each
external part of the secant segment and the entire secant segment equal to the square of the tangent segment.
Feedback
A
B
C
D
Correct!
Check the segments in your multiplication.
You need to multiply, not add.
Check your multiplication.
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
102. ANS: B
When a secant segment and a tangent segment intersect in the exterior of a circle, set the product of each
external part of the secant segment and the entire secant segment equal to the square of the tangent segment.
Feedback
A
B
C
D
Check the segments in your multiplication.
Correct!
You need to multiply, not add.
Check your multiplication.
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
103. ANS: A
When two secant segments intersect in the exterior of a circle, set an equality between the product of each
external segment and the entire segment.
Feedback
A
B
C
D
Correct!
Check your multiplication.
Check the segments in your multiplication.
You need to multiply, not add.
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
104. ANS: A
When two secant segments intersect in the exterior of a circle, set an equality between the product of each
external segment and the entire segment.
Feedback
A
B
C
D
Correct!
Check your multiplication.
You need to multiply, not add.
Check the segments in your multiplication.
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
105. ANS: D
When two secant segments intersect in the exterior of a circle, set an equality between the product of each
external segment and the entire segment. .
Feedback
A
B
C
D
Check the segments in your multiplication.
You need to multiply, not add.
Check your multiplication.
Correct!
PTS: 1
DIF: Average
REF: Lesson 10-7
OBJ: 10-7.2 Find measures of segments that intersect in the exterior of a circle.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
106. ANS: D
When two secant segments intersect in the exterior of a circle, set an equality between the product of each
external segment and the entire segment.
Feedback
A
B
C
D
You need to multiply, not add.
Check the segments in your multiplication.
Check your multiplication.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
REF: Lesson 10-7
10-7.2 Find measures of segments that intersect in the exterior of a circle.
NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 4.2.12 A.3
Find measures of segments that intersect in the exterior of a circle.
Circles | Exterior of Circles