Download Geometry Final Exam Practice and Honors Answer

Geometry Final Exam Practice and Honors
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. 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
____
2. Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary.
a. 1260
c. 360
b. 140
d. 40
Determine whether the quadrilateral is a parallelogram. Justify your answer.
____
3.
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.
Quadrilateral ABCD is a rectangle.
A
B
G
D
C
____
4. If
a. 96
b. –6
and
, find
.
c. 24
d. 48
____
5. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
M
L
36
A
J
B
32
K
a. 4
b. 34
____
c. 68
d. 40
6. 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
Solve each proportion.
____
____
7.
a.
2
559
c.
559
2
b.
43
26
d.
26
43
a.  3
17
c.
7
10
b.
d.  17
3
8.
10
7
Determine whether each pair of figures is similar. Justify your answer.
____
9.
D
C
5.2
12°
117°
A
40°
13.2
13.2
14.2
14.2
40°
E
a.
b.
117°
12°
5.2
F
B
is not similar to
. Corresponding angles are not the same.
because the corresponding angles of each triangle are congruent. The ratio
of the corresponding sides is 1.
c.
is not similar to
. The ratios of the corresponding sides are not the same.
d.
because the corresponding angles of each triangle are congruent. The ratio
of the corresponding sides is 2.
D
____ 10.
A
16.1
5.9
71° 3.5
41°
E
C
55°
7.3
71°
56°
33.58
27.14
F
40°
B
a.
b.
c.
because the corresponding angles are congruent.
is not similar to
because the corresponding angles are not congruent.
because the ratio of the corresponding sides is proportional and the
corresponding angles are congruent.
d.
is not similar to
because the ratio of the corresponding sides is not
proportional.
Determine whether each pair of triangles is similar. Justify your answer.
____ 11.
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.
Find x and the measures of the indicated parts.
____ 12. AB and BC
a.
b.
____ 13. AB
c.
d.
a.
b.
c.
d.
____ 14. AB
a.
c.
b.
d.
____ 15.
BD and CE
a.
c.
b.
d.
____ 16. 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
____ 17.
if
perimeter of
A
Q
P
B
R
C
a. 72
b. 18
c. 108
d. 24
____ 18. Find PS if
is an altitude of
A
12
P
10
16
Q
B
D
is an altitude of
S
R
C
a. 7.5
b. 19.2
c. 4.62
d. 19.5
____ 19. Fran used a graphics program to reduce a digital image. The original dimensions of the image were 11 cm by
10 cm. She used a scale factor of 0.6. What are the dimensions of the reduction?
a. 11.2 cm by 8.7 cm
b. 4.2 cm by 3.4 cm
c. 4.3 cm by 9.8 cm
d. 6.6 cm by 6 cm
____ 20. Find the geometric mean between each pair of numbers.
and
a. 22.5
c. 464
b. 3 5
d. 4 29
____ 21. Find the measure of the
.
A
8
D
15
B
C
a. 2 30
b. 11.5
c.
23
d. 120
____ 22. Find x, y, and z.
y
z
x
3
13
a. x  53.3, y  56.3, z 12.6
b. x  56.3, y  12.6, z 53.3
c. x  12.6, y  53.3, z 56.3
d. x  12.6, y  53.3, z 56.3
____ 23. Find x.
37
x
15
a. 22
c. 1144
b. 2 286
d.
1594
____ 24. Find x and y.
x
60°
24
y
a.
c.
b.
d.
____ 25. Find x and y.
x
60°
3
30°
y
a.
c.
b.
d.
____ 26. A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5° for the next 40
ground miles. About how far above sea level is the rocket ship after its climb?
a. 2.4 mi
c. 653.9 mi
b. 4.4 mi
d. 655.9 mi
A landscaper is making a retaining wall to shore up the side of a hill. To ensure against collapse, the wall
should make an angle 75° with the ground.
____ 27. If the wall is 25 feet, what is the height of the hill?
a. 6.5 ft
c. 25.9 ft
b. 24.1 ft
d. 93.3 ft
____ 28. If the wall is 15 feet, what is the height of the hill?
a. 55.98 ft
c. 14.49 ft
b. 15.53 ft
d. 3.88 ft
____ 29. How far from the base of the hill is the base of a 25-foot slanted wall?
a. 6.5 ft
c. 93.3 ft
b. 24.1 ft
d. 96.6 ft
____ 30. How far from the base of the hill is the base of a 15-foot slanted wall?
a. 3.88 ft
c. 55.98 ft
b. 14.49 ft
d. 57.96 ft
____ 31. Pat was flying a kite when the string broke and the kite fell to the ground. Pat is 36 yards lower than the kite.
The distance from Pat to the kite is 200 yards. What is the angle of elevation?
a. 10.2°
c. 79.6°
b. 10.4°
d. 79.8°
____ 32. After flying at an altitude of 500 meters, a hang glider starts to descend when the ground distance from the
landing pad is 15 kilometers. What is the angle of depression for this part of the flight?
a. 1.7°
c. 88.1°
b. 1.9°
d. 88.3°
The radius, diameter, or circumference of a circle is given. Find the missing measures. Round to the nearest
hundredth if necessary.
____ 33. d = 22.3 km, r = ? , C = ?
a. r = 44.6 km, C = 35.03 km
b. r = 11.15 km, C = 35.03 km
c. r = 11.15 km, C = 70.06 km
d. r = 44.6 km, C = 70.06 km
____ 34. Find the exact circumference of the circle.
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
____ 35.
a. 140
b. 120
____ 36.
c. 130
d. 150
a. 50
b. 60
c. 130
d. 40
a. 180
b. 90
c. 60
d. 30
a. 50
b. 40
c. 60
d. 30
a. 170
b. 160
c. 150
d. 140
a. 110
b. 120
c. 130
d. 140
____ 37.
____ 38.
____ 39.
____ 40.
____ 41. In
,
,
= 7x,
= 5x + 12, and
B
F
A
C
D
E
Find m arc
a. 56
b. 46
____ 42. In
,
.
c. 50
d. 49
and AE = 10.
and
are diameters.
D
E
A
C
F
8
B
Find m
a. 14
b. 12
____ 43.
G
.
c. 10
d. 16
B
C
1
A
If
a. 45
b. 70
D
= 35,
= 100, and
= 100, find
c. 35
d. 90
____ 44. Find x. Assume that segments that appear tangent are tangent.
A
13
5
C
a. 9
b. 7
x
B
c. 12
d. 17
.
____ 45. Find x. Assume that segments that appear tangent are tangent.
F
4
8
x
D
E
a. 7
b. 6
c. 14
d. 5
____ 46. 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.
____ 47.
1
100°
130°
a. 230
b. 115
c. 130
d. 125
____ 48.
105
3
135
a. 60
b. 70
c. 80
d. 65
2 x°
____ 49.
2 x°
4 x°
7
4 x°
a. 92
b. 95
c. 94
d. 90
____ 50.
8
220°
a. 90
b. 180
c. 220
d. 110
Find x. Assume that any segment that appears to be tangent is tangent.
____ 51.
x°
10°
60°
a. 15
b. 35
c. 25
d. 45
____ 52.
30°
90°
a. 15
b. 30
2 x°
c. 20
d. 10
____ 53.
4x°
88°
12x°
a. 22
b. 9
c. 18
d. 11
Find x. Round to the nearest tenth if necessary.
____ 54.
6
3
a. 5
b. 6
x
2
c. 3
d. 4
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
____ 55.
6
2
4
x
a. 8
b. 10
c. 3
d. 4
____ 56. Write an equation for a circle with center at (–6, 10) and diameter 6.
a.
c.
b.
d.
Graph the equation.
____ 57.
y
a.
8
7
6
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
y
c.
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
x
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
1 2 3 4 5 6 7 8
x
y
b.
y
d.
8
7
6
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
x
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
1 2 3 4 5 6 7 8
Find the lateral area of each prism. Round to the nearest tenth if necessary.
____ 58. The dimension labeled 10 is the height of the prism.
4
10
5
a. 120 units2
b. 160 units2
c. 180 units2
d. 220 units2
____ 59.
5
8
6
a. 146.4 units2
b. 150.5 units2
c. 165.4 units2
d. 180.5 units2
x
____ 60.
8
8
8
2
c. 320 units2
d. 384 units2
a. 64 units
b. 256 units2
Find the volume of the prism. Round to the nearest tenth if necessary.
____ 61.
2 in.
10 in.
13 in.
a. 273 in 3
b. 50 in 3
c. 260 in 3
d. 176 in 3
Find the volume of the cylinder. Use 3.14 for . Round to the nearest tenth.
____ 62.
12.8 in.
14 in.
a. 7877.6 in 3
b. 627.2 in 3
c. 281.3 in 3
d. 1969.4 in 3
____ 63. Find the volume of the sphere. Use 3.14 for . Round to the nearest tenth.
17 m
a. 302.5 m3
b. 642.8 m3
c. 1,928.4 m3
d. 2,571.1 m3
Short Answer
64. In a botanical garden, a regular octagonal greenhouse was designed especially for orchids. Find the sum of the
measures of the interior angles and an exterior angle of the greenhouse.
65. Find the measure of each interior angle of nonagon in which the measure of the interior angles are
,
,
,
,
,
,
,
.
Use the parallelogram ABCD to find the measure or value as indicated.
5x -7
D
72 °
3 y +7
26.4
°
71
F
5q - 0.5
A
18.5
C
44.5
4p -2
16.9
45 °
B
66.
67.
68.
69. p
70.
71. For isosceles trapezoid PQRS, L and M are the midpoints of the legs. Find LM,
, and
.
,
26
S
L
R
M
57 °
P
48
Q
72. A quilt design is based on the pattern shown below. Find the value of x.
x
5
5
45°
73. How high is the end of a 70-foot ramp when it is tipped to an angle of
height
of ramp
70 ft
45°
74. Find the value of x in the figure below.
x
35°
60
75. Beth is measuring the height of a tree. She stands 37 feet from the base of the tree. The angle formed by the
ground and the line to the top of the tree is
Find the height of the tree.
h
75°
37 ft
76. In the figure below, A and B represent the top and the bottom of a large balloon floating directly above the
street. Arnold is standing 40 feet from a point on the street directly beneath the balloon. Find the height h of
the balloon.
77. Arthur cuts a
slice from a pizza 14 inches in diameter. Find the length of
78. Find the values of y and z.
A
z°
y°
D
B
110°
75°
C
.
Geometry Final Exam Practice and Honors
Answer Section
MULTIPLE CHOICE
1. ANS: 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:
STA:
TOP:
KEY:
2. ANS:
1
DIF: Average
REF: Lesson 6-1
6-1.1 Find the sum of the measures of the interior angles of a polygon.
MA.912.G.2.2 | MA.912.G.3.4
Find the sum of the measures of the interior angles of a polygon.
Interior Angles | Polygons
D
To find the size of each exterior angle of a regular polygon, use the formula
.
Feedback
A
B
C
D
This is the sum of the interior angles.
This is the value of each interior angle.
This is the sum of all of the exterior angles not each individual angle.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 6-1
OBJ: 6-1.2 Find the sum of the measures of the exterior angles of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
TOP: Find the sum of the measures of the exterior angles of a polygon.
KEY: Exterior Angles | Polygons
3. 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.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3
TOP: Recognize the conditions that ensure a quadrilateral is a parallelogram.
KEY: Quadrilaterals | Parallelograms | Determining a Parallelogram
4. 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:
OBJ:
STA:
TOP:
KEY:
5. ANS:
1
DIF: Average
REF: Lesson 6-4
6-4.1 Recognize and apply properties of rectangles.
MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
Recognize and apply properties of rectangles.
Rectangles | Properties of Rectangles
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.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
TOP: Recognize and apply the properties of trapezoids.
KEY: Trapezoids | Properties of Trapezoids
6. 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.
STA: MA.912.D.11.5
TOP: Write ratios. KEY: Ratios
7. ANS: D
Find the cross products. Multiply. Divide each side by the coefficient of the variable.
Feedback
A
Remember to cross multiply.
B
C
D
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.
STA: MA.912.D.11.5
TOP: Use properties of proportions.
KEY: Proportions
8. 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: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.2 Use properties of proportions.
STA: MA.912.D.11.5
TOP: Use properties of proportions.
KEY: Proportions
9. ANS: B
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
Feedback
A
B
C
D
Check the size of the angles.
Correct!
Determine the ratio of the corresponding sides.
Check the similarity statement.
PTS: 1
DIF: Basic
REF: Lesson 7-2
OBJ: 7-2.1 Identify similar figures.
STA: MA.912.G.2.3 | MA.912.G.3.3 | MA.912.G.3.4
TOP: Identify similar figures.
KEY: Similar Figures
10. ANS: B
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
Feedback
A
B
C
D
In order for the triangles to be similar, the corresponding angles must be congruent and
the ratio of corresponding sides must be proportional.
Correct!
Are the angles congruent?
Check the ratio of the corresponding sides.
PTS:
STA:
KEY:
11. ANS:
1
DIF: Basic
REF: Lesson 7-2
MA.912.G.2.3 | MA.912.G.3.3 | MA.912.G.3.4
Similar Figures
A
OBJ: 7-2.1 Identify similar figures.
TOP: Identify similar figures.
So,
.
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.
STA: MA.912.G.4.6 | MA.912.G.4.8 | MA.912.G.2.3 | MA.912.G.4.4
TOP: Identify similar triangles.
KEY: Similar Triangles
12. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Check your ratio.
What are the values of AB and BC?
Check your addition.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: MA.912.G.4.6 | MA.912.G.4.8 | MA.912.G.2.3 | MA.912.G.4.4
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
13. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Which side is AB?
Check your operations.
Which side does the question ask you to find?
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: MA.912.G.4.6 | MA.912.G.4.8 | MA.912.G.2.3 | MA.912.G.4.4
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
14. ANS: B
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Check your multiplication.
Correct!
Check your ratio.
Check your multiplication.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: MA.912.G.4.6 | MA.912.G.4.8 | MA.912.G.2.3 | MA.912.G.4.4
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
15. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Check your addition.
Check the ratios.
Check the ratios and your multiplication.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: MA.912.G.4.6 | MA.912.G.4.8 | MA.912.G.2.3 | MA.912.G.4.4
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
16. 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.
STA: MA.912.G.4.5 | MA.912.G.4.6 | MA.912.G.4.4
TOP: Use proportional parts of triangles.
KEY: Proportional Parts | Triangles
17. 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.
STA: MA.912.G.2.3 | MA.912.G.4.6 | MA.912.G.4.4
TOP: Recognize and use proportional relationships of corresponding perimeters of similar triangles.
KEY: Proportional Relationships | Triangles
18. 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
Correct!
Interchange the numerator and the denominator on either side of the proportion.
C
D
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.
STA: MA.912.G.2.3 | MA.912.G.4.6 | MA.912.G.4.4
TOP: Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians
of similar triangles. KEY: Proportional Relationships | Triangles
19. ANS: D
PTS: 1
DIF: Basic
REF: Lesson 7-6
OBJ: 7-6.1 Identify similarity transformations.
STA: MA.912.G.2.4 | MA.912.G.2.6
TOP: Similarity transformations.
KEY: dilation
20. 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.
STA: MA.912.G.4.5 | MA.912.G.5.2 | MA.912.G.4.4 | MA.912.G.4.6 | MA.912.G.5.4
TOP: Find the geometric mean between two numbers.
KEY: Geometric Mean
21. 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.
STA: MA.912.G.4.5 | MA.912.G.5.2 | MA.912.G.4.4 | MA.912.G.4.6 | MA.912.G.5.4
TOP: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse.
KEY: Triangles | Altitudes | Hypotenuse
22. ANS: D
The altitude is the geometric mean between the measures of the two segments of the hypotenuse.
Feedback
A
B
C
D
What is the value of y?
What is the value of x?
How do you find the geometric mean?
Correct!
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.
STA: MA.912.G.4.5 | MA.912.G.5.2 | MA.912.G.4.4 | MA.912.G.4.6 | MA.912.G.5.4
TOP: Solve problems involving relationships between parts of a right triangle and the altitude hypotenuse.
KEY: Triangles | Altitudes | Hypotenuse
23. ANS: B
The sum of the squares of the two sides is equal to the square of the hypotenuse.
Feedback
A
B
C
D
Remember to square the numbers.
Correct!
Remember to find the square root.
Which side is the hypotenuse?
PTS: 1
DIF: Basic
REF: Lesson 8-2
OBJ: 8-2.1 Use the Pythagorean Theorem.
STA: MA.912.G.5.1 | MA.912.G.5.4
TOP: Use the Pythagorean Theorem.
KEY: Pythagorean Theorem
24. 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.
STA: MA.912.G.5.3 | MA.912.G.5.4 | MA.912.G.5.1
TOP: Use properties of 30°-60°-90° triangles.
KEY: Triangles | 30-60-90 Triangles
25. 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
Switch the x and y values.
How do you find the length of the side opposite the 60angle?
How do you find the length of the side opposite the 30 angle?
Correct!
PTS: 1
DIF: Average
REF: Lesson 8-3
OBJ: 8-3.2 Use properties of 30°-60°-90° triangles.
STA: MA.912.G.5.3 | MA.912.G.5.4 | MA.912.G.5.1
TOP: Use properties of 30°-60°-90° triangles.
KEY: Triangles | 30-60-90 Triangles
26. 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
Remember to include the initial height of two miles.
Correct!
C
D
Which trigonometric ratio should be used?
Which trigonometric ratio should be used?
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.2 Solve problems using trigonometric ratios.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve problems using trigonometric ratios.
KEY: Trigonometric Ratios | Solve Problems
27. 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 cosine ratio.
Correct!
Check the setup of the ratio.
Do not use the tangent ratio.
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.2 Solve problems using trigonometric ratios.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve problems using trigonometric ratios.
KEY: Trigonometric Ratios | Solve Problems
28. 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
Do not use the tangent ratio.
What is the sine ratio?
Correct!
Do not use the cosine ratio.
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.2 Solve problems using trigonometric ratios.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve problems using trigonometric ratios.
KEY: Trigonometric Ratios | Solve Problems
29. 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 sine ratio.
Do not use the tangent ratio.
What is the cosine ratio?
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 8-4
8-4.2 Solve problems using trigonometric ratios.
Solve problems using trigonometric ratios.
Trigonometric Ratios | Solve Problems
STA: MA.912.T.2.1 | MA.912.G.5.4
30. 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 sine ratio.
Do not use the tangent ratio.
What is the cosine ratio?
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.2 Solve problems using trigonometric ratios.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve problems using trigonometric ratios.
KEY: Trigonometric Ratios | Solve Problems
31. 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.
STA: LA.1112.1.6.2 | MA.912.G.5.4
TOP: Solve problems involving angles of elevation.
KEY: Angle of Elevation
32. 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 sine ratio.
Correct!
Check the ratio.
Remember to convert kilometers to meters.
PTS: 1
DIF: Average
REF: Lesson 8-5
OBJ: 8-5.2 Solve problems involving angles of depression.
TOP: Solve problems involving angles of depression.
33. ANS: C
radius = diameter  2
Circumference = (2  radius   or (diameter  
Feedback
A
B
C
D
Check both your radius and circumference calculations.
Check your circumference calculation.
Correct!
Check your radius calculation.
STA: LA.1112.1.6.2 | MA.912.G.5.4
KEY: Angle of Depression
PTS: 1
DIF: Basic
REF: Lesson 10-1
OBJ: 10-1.1 Identify and use parts of circles.
STA: MA.912.G.6.1 | MA.912.G.6.2 | MA.912.G.6.5
TOP: Identify and use parts of circles.
KEY: Circles | Parts of Circles
34. 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:
OBJ:
STA:
TOP:
35. ANS:
1
DIF: Average
REF: Lesson 10-1
10-1.2 Solve problems involving the circumference of a circle.
MA.912.G.6.1 | MA.912.G.6.2 | MA.912.G.6.5
Solve problems involving the circumference of a circle.
KEY: Circles | Circumference
C
forms a linear pair with
, so their sum is 180.
Feedback
A
B
C
D
Check your subtraction.
How many degrees are in a linear pair?
Correct!
Check your subtraction.
PTS:
OBJ:
STA:
TOP:
KEY:
36. ANS:
1
DIF: Basic
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
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:
STA:
TOP:
KEY:
37. ANS:
1
DIF: Basic
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
B
is a right angle, so its measure is 90.
Feedback
A
B
C
D
It's a right angle.
Correct!
It's a right angle.
What is the measure of a right angle?
PTS:
OBJ:
STA:
TOP:
KEY:
38. ANS:
1
DIF: Basic
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
B
is complementary with
.
Feedback
A
B
C
D
Did you subtract carefully?
Correct!
With what angle is it complementary?
What is the measure of angle BAE?
PTS:
OBJ:
STA:
TOP:
KEY:
39. ANS:
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
Major Arcs | Minor Arcs | Semicircles | Central Angles
D
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.
What is the measure of angle DAE?
Correct!
PTS:
OBJ:
STA:
TOP:
KEY:
40. ANS:
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
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:
STA:
TOP:
KEY:
41. ANS:
Since
1
DIF: Average
REF: Lesson 10-2
10-2.1 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
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.
STA: MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
TOP: Find arc length.
KEY: Arcs | Arc Length
42. 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:
OBJ:
STA:
TOP:
KEY:
43. ANS:
1
DIF: Average
REF: Lesson 10-3
10-3.1 Recognize and use relationships between arcs and chords.
MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.4
Recognize and use relationships between arcs and chords.
Arcs | Chords | Diameters
A
The measure of
is 2 
360 – (
+
+
. Since the full circle measures 360, then
). Finally, since
is an inscribed angle for
Feedback
A
B
C
D
Correct!
Focus on
.
Can you find the measure of
?
Inscribed angles are half the measure of the arc.
PTS: 1
DIF: Average
REF: Lesson 10-4
is
, its measure is m
.
.
OBJ: 10-4.1 Find measures of inscribed angles.
STA: MA.912.G.6.1 | MA.912.G.6.4 | MA.912.G.6.3
TOP: Find measures of inscribed angles.
KEY: Inscribed Angles | Measure of Inscribed Angles
44. 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.
STA: MA.912.G.6.1 | MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Use properties of tangents.
KEY: Tangents
45. ANS: B
The triangle shown is a right triangle since the tangent segment, FE, intersects a radius, DE, which always
results in a right angle. So to solve for x, use the Pythagorean Theorem. Note that
since they are
both radii of the same circle.
Feedback
A
B
C
D
Use the Pythagorean Theorem and
Correct!
Is the triangle a right?
Use the Pythagorean Theorem and
.
.
PTS: 1
DIF: Average
REF: Lesson 10-5 OBJ: 10-5.1 Use properties of tangents.
STA: MA.912.G.6.1 | MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Use properties of tangents.
KEY: Tangents
46. 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.
STA: MA.912.G.6.1 | MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Solve problems involving circumscribed polygons.
KEY: Circumscribed Polygons
47. 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.
Feedback
A
B
C
D
Did you add the intercepted arcs?
Correct!
Add the intercepted arcs and divide by 2.
Did you divide correctly?
PTS: 1
DIF: Basic
REF: Lesson 10-6
OBJ: 10-6.1 Find measures of angles formed by lines intersecting on or inside a circle.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
48. 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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
49. 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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
50. ANS: D
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 220.
Feedback
A
B
C
D
How is the measure of the angle related to the measure of the intercepted arc?
Find half the measure of the intercepted arc.
Should you have divided by two?
Correct!
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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting on or inside a circle.
KEY: Measure of Angles | Circles
51. ANS: C
When two secants 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.
Use subtraction, not addition.
Correct!
Did you subtract carefully?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
52. ANS: A
When two secants 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 take one-half of the positive difference of the measures of the intercepted arcs?
Check your subtraction.
Did you subtract carefully?
PTS: 1
DIF: Average
REF: Lesson 10-6
OBJ: 10-6.2 Find measures of angles formed by lines intersecting outside the circle.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
53. 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
Correct!
Did you subtract carefully?
What is the relationship between the angle and the intercepted arcs?
D
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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.6.2
TOP: Find measures of angles formed by lines intersecting outside the circle.
KEY: Measure of Angles | Circles
54. 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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.4.5
TOP: Find measures of segments that intersect in the interior of a circle.
KEY: Circles | Interior of Circles
55. 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.
STA: MA.912.G.6.4 | MA.912.G.6.3 | MA.912.G.4.5
TOP: Find measures of segments that intersect in the exterior of a circle.
KEY: Circles | Exterior of Circles
56. ANS: A
The equation of a circle is
where (h, k) is the center and r is the radius. In this
problem, the center is given, but not the radius. The radius is one-half the diameter, so first divide the given
diameter by 2 to get the radius.
Feedback
A
B
C
D
Correct!
You need to square the radius, not the diameter.
You need the opposite signs on your center coordinates.
You need the opposite signs on your center coordinates and you need to square the
radius, not the diameter.
PTS: 1
DIF: Average
REF: Lesson 10-8
OBJ: 10-8.1 Write the equation of a circle.
STA: MA.912.G.6.6 | MA.912.G.6.7
TOP: Write the equation of a circle.
KEY: Circles | Equation of Circles
57. ANS: A
The graph of an equation of the form
will be a circle centered at (0, 0) and with radius r.
Feedback
A
B
C
D
Correct!
Check your radius.
Check your radius.
Check your radius.
PTS: 1
DIF: Basic
REF: Lesson 10-8
OBJ: 10-8.2 Graph a circle on the coordinate plane.
STA: MA.912.G.6.6 | MA.912.G.6.7
TOP: Graph a circle on the coordinate plane.
KEY: Circles | Graph Circles | Coordinate Plane
58. ANS: C
The lateral area is the sum of the areas of the lateral faces of the prism. If a right prism has a lateral area of L
square units, a height of h units, and each base has a perimeter of P units, then L = Ph. The perimeter is the
sum of all of the sides of the base.
Feedback
A
B
C
D
Lateral area is perimeter of the base times the height.
Lateral area is perimeter of the base times the height.
Correct!
Find the lateral area, not the surface area.
PTS: 1
DIF: Average
REF: Lesson 12-2 OBJ: 12-2.1 Find lateral areas of prisms.
STA: MA.912.G.7.5 | MA.912.G.7.7 | MA.912.G.7.2
TOP: Find lateral areas of prisms.
KEY: Lateral Area | Prisms | Lateral Area of Prisms
59. ANS: B
The lateral area is the sum of the areas of the lateral faces of the prism. If a right prism has a lateral area of L
square units, a height of h units, and each base has a perimeter of P units, then L = Ph. The perimeter is the
sum of all of the sides of the base.
Feedback
A
B
C
D
What is the base of the prism?
Correct!
Lateral area is perimeter of the base times the height.
Find the lateral area, not the surface area.
PTS: 1
DIF: Average
REF: Lesson 12-2 OBJ: 12-2.1 Find lateral areas of prisms.
STA: MA.912.G.7.5 | MA.912.G.7.7 | MA.912.G.7.2
TOP: Find lateral areas of prisms.
KEY: Lateral Area | Prisms | Lateral Area of Prisms
60. ANS: B
The lateral area is the sum of the areas of the lateral faces of the prism. If a right prism has a lateral area of L
square units, a height of h units, and each base has a perimeter of P units, then L = Ph. The perimeter is the
sum of all of the sides of the base.
Feedback
A
B
C
D
Lateral area is perimeter of the base times the height.
Correct!
Lateral area is perimeter of the base times the height.
Find the lateral area, not the surface area.
PTS: 1
DIF: Average
REF: Lesson 12-2
STA: MA.912.G.7.5 | MA.912.G.7.7 | MA.912.G.7.2
KEY: Lateral Area | Prisms | Lateral Area of Prisms
61. ANS: C
The volume of a rectangular prism is found by the formula
OBJ: 12-2.1 Find lateral areas of prisms.
TOP: Find lateral areas of prisms.
.
Feedback
A
B
C
D
How do you find the volume of a rectangular prism?
What is the formula for the volume of a rectangular prism?
Correct!
The volume is the product of the three dimensions.
PTS: 1
DIF: Basic
REF: Lesson 12-4 OBJ: 12-4.1 Find volumes of prisms.
STA: MA.912.G.7.5 | MA.912.G.7.7
TOP: Find volumes of prisms.
KEY: Volume | Prisms | Volume of Prisms
62. ANS: D
The volume of a cylinder is found by the formula
. In this figure, the height and diameter
are given. To find the radius, divide the diameter by 2.
Feedback
A
B
C
D
What is the formula for the volume of a cylinder?
How do you find the volume of a cylinder?
What is the radius of the base?
Correct!
PTS: 1
DIF: Average
REF: Lesson 12-4 OBJ: 12-4.2 Find volumes of cylinders.
STA: MA.912.G.7.5 | MA.912.G.7.7
TOP: Find volumes of cylinders.
KEY: Volume | Cylinders | Volume of Cylinders
63. ANS: D
The volume of a sphere is found by the formula
. In this problem, the radius or diameter is
given. To find the radius from the diameter, simply divide by 2.
Feedback
A
B
You need to cube the radius, not square it.
C
You need to multiply your answer by
D
Correct!
The volume formula has
in it, not .
.
PTS: 1
DIF: Average
REF: Lesson 12-6
STA: MA.912.G.7.5 | MA.912.G.7.7 | MA.912.G.7.4
KEY: Volume | Spheres | Volume of Spheres
OBJ: 12-6.3 Find volumes of spheres.
TOP: Find volumes of spheres.
SHORT ANSWER
64. ANS:
1080, 45
To find the sum of the measures of the interior angles of a regular polygon, use the formula
To find the measure of each exterior angle of a regular polygon, use the formula
.
.
PTS: 1
DIF: Advanced
REF: Lesson 6-1
OBJ: 6-1.3 Find the sum of the measure of the interior and exterior measures of a polygon.
STA: MA.912.G.2.2 | MA.912.G.3.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
65. ANS:
168, 132, 163, 157, 162, 67, 148, 91, 172
Add all the interior angles in terms of variables, and equate to
to find the measure of each angle.
PTS:
OBJ:
STA:
KEY:
66. ANS:
117
. Substitute the value of that variable
1
DIF: Advanced
REF: Lesson 6-1
6-1.3 Find the sum of the measure of the interior and exterior measures of a polygon.
MA.912.G.2.2 | MA.912.G.3.4
TOP: Solve multi-step problems.
Solve multi-step problems.
, alternate interior angles are congruent.
PTS: 1
DIF: Basic
REF: Lesson 6-2
OBJ: 6-2.3 Recognize and apply properties of the sides and angles of parallelograms and the diagonals of
parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
67. ANS:
63
The sum of the measure of the angles in
is
.
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.3 Recognize and apply properties of the sides and angles of parallelograms and the diagonals of
parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
68. ANS:
109
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.3 Recognize and apply properties of the sides and angles of parallelograms and the diagonals of
parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
KEY: Solve multi-step problems.
69. ANS:
7.1
TOP: Solve multi-step problems.
PTS: 1
DIF: Advanced
REF: Lesson 6-2
OBJ: 6-2.3 Recognize and apply properties of the sides and angles of parallelograms and the diagonals of
parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
70. ANS:
26
The sum of the measure of the angles in
is
.
PTS: 1
DIF: Advanced
REF: Lesson 6-2
OBJ: 6-2.3 Recognize and apply properties of the sides and angles of parallelograms and the diagonals of
parallelograms.
STA: MA.912.G.3.1 | MA.912.G.3.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
71. ANS:
37, 57, 123
To find the median, find the sum of the bases and then divide by two.
To find the adjacent angle, apply the property that the pair of base angles of an isosceles trapezoid is
congruent.
To find the opposite angle, apply the property that the opposite angles of an isosceles trapezoid are
supplementary.
PTS: 1
DIF: Average
REF: Lesson 6-6
OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of
trapezoids.
STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
72. ANS:
In a
PTS:
OBJ:
STA:
KEY:
73. ANS:
triangle, the length of the hypotenuse is
times the length of a leg.
1
DIF: Average
REF: Lesson 8-3
8-3.3 Use properties of 45°-45°-90° and 30°-60°-90° triangles.
MA.912.G.5.3 | MA.912.G.5.4 | MA.912.G.5.1
TOP: Solve multi-step problems.
Solve multi-step problems.
In a
PTS: 1
triangle, the length of the hypotenuse is
DIF: Advanced
REF: Lesson 8-3
times the length of a leg.
OBJ: 8-3.3 Use properties of 45°-45°-90° and 30°-60°-90° triangles.
STA: MA.912.G.5.3 | MA.912.G.5.4 | MA.912.G.5.1
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
74. ANS:
about 42
Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the
answer.
PTS: 1
DIF: Basic
REF: Lesson 8-4
OBJ: 8-4.3 Find trigonometric ratios using right triangles and solve problems.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
75. ANS:
about 138.1 ft
Determine which trigonometric ratio should be used to solve. Substitute the numbers given. Solve for the
answer.
PTS: 1
DIF: Average
REF: Lesson 8-4
OBJ: 8-4.3 Find trigonometric ratios using right triangles and solve problems.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
76. ANS:
about 61 ft
Determine which trigonometric ratios should be used to solve. Substitute the numbers given. Solve for the
answer.
PTS: 1
DIF: Advanced
REF: Lesson 8-4
OBJ: 8-4.3 Find trigonometric ratios using right triangles and solve problems.
STA: MA.912.T.2.1 | MA.912.G.5.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
77. ANS:
about 3.7 in.
PTS: 1
DIF: Average
REF: Lesson 10-2
OBJ: 10-2.3 Recognize major arcs, minor arcs, semicircles, and central angles, and their measures. Find
arc length.
STA: MA.912.G.6.3 | MA.912.G.6.2 | MA.912.G.6.5 | MA.912.G.6.4
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
78. ANS:
;
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
PTS: 1
DIF: Average
REF: Lesson 10-4
OBJ: 10-4.3 Find measures of inscribed angles and angles of inscribed polygons.
STA: MA.912.G.6.1 | MA.912.G.6.4 | MA.912.G.6.3
KEY: Solve multi-step problems.
TOP: Solve multi-step problems.