Download ExamView - 2nd semester exam review

Name: ________________________ Class: ___________________ Date: __________
ID: A
2nd Semester Exam Review - Geometry CP
3. Which statement can you use to conclude that
quadrilateral XYZW is a parallelogram?
1. Complete this statement: A polygon with all sides
the same length is said to be ____.
a. regular
b. equilateral
c. equiangular
d. convex
2. WXYZ is a parallelogram. Name an angle congruent
to ∠WXY.
a.
b.
c.
d.
WZ ≅ XY and XW ≅ WZ
WZ ≅ ZY and XW ≅ YZ
WZ ≅ XY and XW ≅ YZ
WN ≅ NZ and YN ≅ NX
4. Classify the figure in as many ways as possible.
a.
b.
c.
d.
∠WZX
∠WZY
∠YZX
∠XYZ
a.
b.
c.
d.
rectangle, square, quadrilateral, parallelogram,
rhombus
rectangle, square, parallelogram
rhombus, quadrilateral, square
square, rectangle, quadrilateral
5. The two rectangles are similar. Which is the correct proportion for corresponding sides?
a.
12
8
=
24
4
b.
12
4
=
24
8
c.
12
4
1
=
8
24
d.
4
12
=
24
8
Name: ________________________
ID: A
7.
Find the value of x. If necessary, round your
answer to the nearest tenth. The figure is not
drawn to scale.
6.
a.
b.
c.
d.
13.27
17.55
10.58
176
8. AB = 15, BC = 9, and CD = 10
2
Name: ________________________
ID: A
Determine whether each pair of triangles is
similar. Justify your answer.
9.
Find x and the measures of the indicated parts.
10. AB
11. AB
12.
If m∠BDC = 35, m arc AB = 100, and
m arc CD = 100, find m∠1.
3
Name: ________________________
ID: A
Find x. Assume that any segment that appears to be
tangent is tangent.
13.
16.
If m∠1 = 2x + 2, m∠2 = 9x, find m∠1.
14. Find x. Assume that segments that appear tangent
are tangent.
17.
15. Find x. Assume that segments that appear tangent
are tangent.
4
Name: ________________________
ID: A
21. For the parallelogram, if m∠2 = 5x − 30 and
m∠4 = 3x − 10, find m∠3. The diagram is not to
scale.
Find x. Round to the nearest tenth if necessary.
Assume that segments that appear to be tangent are
tangent.
18.
22. LMNO is a parallelogram. If NM = x + 14 and OL =
2x + 7, find the value of x and then find NM and
OL.
19. Find the values of the variables in the
parallelogram. The diagram is not to scale.
23. Find values of x and y for which ABCD must be a
parallelogram. The diagram is not to
scale.
20. In the parallelogram, m∠QRP = 57 and
m∠PRS = 62. Find m∠PQR. The diagram is not to
scale.
5
Name: ________________________
ID: A
27. In quadrilateral ABCD, AE = x + 14 and
BE = 3x − 18 . For what value of x is ABCD a
rectangle?
24. In the rhombus,
m∠1 = 3x, m∠2 = x + y, and m∠3 = 3z. Find
the value of each variable. The diagram is not to
scale.
28. Find the values of a and b.The diagram is not to
scale.
25. Find the measure of the numbered angles in the
rhombus. The diagram is not to scale.
29. ∠J and ∠M are base angles of isosceles trapezoid
JKLM. If m∠J = 15x + 6, and
m∠M = 14x + 14, find m∠K.
26. In rectangle KLMN, KM = 5x + 16 and LN = 58.5.
Find the value of x.
30. LM is the midsegment of
ABCD.
AB = 85 and DC = 119. What is LM?
6
Name: ________________________
ID: A
ABCD.
31. LM is the midsegment of
AB = x + 8, LM = 4x + 3, and DC = 173. What is
the value of x?
What is the solution of each proportion?
32.
3
a
=
15
33.
40
3y − 8
12
=
y
5
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
34.
7
Name: ________________________
ID: A
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
36. Are the triangles similar? How do you know?
35.
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you
used.
37.
38. Use the information in the diagram to determine
the height of the tree to the nearest foot.
8
Name: ________________________
ID: A
39. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the
flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet
above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to
the nearest tenth of a foot.
40. Campsites F and G are on opposite sides of a lake.
A survey crew made the measurements shown on
the diagram. What is the distance between the two
campsites? The diagram is not to scale.
41. What is the value of x, given that PQ Ä BC ?
Find the length of the missing side. The triangle is not drawn to scale.
42.
43. Triangle ABC has side lengths 12, 35, and 37. Do
the side lengths form a Pythagorean triple?
Explain.
9
Name: ________________________
ID: A
Find the length of the missing side. Leave your answer in simplest radical form.
47. Find the length of the leg. If your answer is not an
integer, leave it in simplest radical form.
44.
45. A triangle has side lengths of 38 in, 22 in, and 39
in. Classify it as acute, obtuse, or right.
48. The area of a square garden is 128 m2. How long is
the diagonal?
46. In triangle ABC, ∠A is a right angle and m∠B =
45°. Find BC. If your answer is not an integer,
leave it in simplest radical form.
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
51. Find the missing value to the nearest hundredth.
49.
52. Write the ratios for sin A and cos A.
50.
10
Name: ________________________
ID: A
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
54.
53.
Find the value of x. Round to the nearest tenth.
55.
58.
56.
59. Find the value of w, then x. Round lengths of
segments to the nearest tenth.
57.
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Name: ________________________
ID: A
Find the value of x. Round to the nearest degree.
61.
60.
Find the value of x to the nearest degree.
62.
63.
What is the description of ∠1 as it relates to the situation shown?
64. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance
door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the
entrance door?
12
Name: ________________________
ID: A
Find the area. The figure is not drawn to scale.
66.
65.
Find the area of the trapezoid. Leave your answer in simplest radical form.
67.
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the
second. The figures are not drawn to scale.
68.
69. The trapezoids are similar. The area of the smaller
trapezoid is 131 m 2 . Find the area of the larger
trapezoid to the nearest whole number.
70. Find the similarity ratio and the ratio of perimeters
for two regular pentagons with areas of 25 cm2
and 64 cm2.
13
Name: ________________________
ID: A
Find the circumference. Leave your answer in terms of π .
71.
Find the area of the circle. Leave your answer in terms of π .
72.
Find the surface area of the cylinder in terms of π .
73.
14
Name: ________________________
ID: A
Find the volume of the given prism. Round to the nearest tenth if necessary.
74.
Find the volume of the cylinder in terms of π .
75.
Find the volume of the square pyramid shown.
Round to the nearest tenth if necessary.
77.
76. Find the volume of the composite space figure to
the nearest whole number.
15
Name: ________________________
ID: A
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
78.
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
79.
Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.
80.
82. Find the similarity ratio of a cube with volume 216
ft 3 to a cube with volume 2744 ft 3 .
83. The volumes of two similar solids are 729 m 3 and
125 m 3 . The surface area of the larger solid is
324 m 3 . What is the surface area of the smaller
solid?
81. Find the similarity ratio of a prism with the surface
area of 81 m 2 to a similar prism with the surface
area of 196 m 2 .
16
Name: ________________________
ID: A
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.
(Figures are not drawn to scale.)
84. m∠O = 145
87. JK , KL, and LJ are all tangent to O (not drawn to
scale). JA = 13, AL = 9, and
CK = 11. Find the perimeter of ∆JKL.
85. m∠P = 23
88. NA ≅ PA , MO ⊥ NA, RO ⊥ PA , MO = 7 ft
What is PO?
86. AB is tangent to circle O at B. Find the length of
the radius r for AB = 7 and AO = 8.6. Round to the
nearest tenth if necessary. The diagram is not to
scale.
17
Name: ________________________
ID: A
Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.
92. Find x. (The figure is not drawn to scale.)
89.
90.
93. Find m∠BAC. (The figure is not drawn to scale.)
91. Find the measure of ∠BAC. (The figure is not
drawn to scale.)
18
Name: ________________________
ID: A
94. m∠R = 42. Find m∠O. (The figure is not drawn to
scale.)
95. If mBY = 40, what is m∠YAC? (The figure is not
drawn to scale.)
96. mDE = 106 and mBC = 70. Find m∠A. (The figure is not drawn to scale.)
19
Name: ________________________
ID: A
100. Find the diameter of the circle for BC = 11 and DC
= 27. Round to the nearest tenth.
(The diagram is not drawn to scale.)
97. Find the value of x for mAB = 31 and mCD = 27.
(The figure is not drawn to scale.)
98. Find m∠D for m∠B = 74. (The figure is not drawn
to scale.)
99. Find the measure of value of AB for m∠P = 48.
(The figure is not drawn to scale.)
20
ID: A
2nd Semester Exam Review - Geometry CP
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B
B
C
A
B
A
30
11.6
yes; ∆EDF ∼ ∆BCA by SSS Similarity
x = 7, AB = 20
3
x = , AB = 3
2
45
18
6
5
15
25
2.3
x = 27, y = 52, z = 101
61
160
x = 7, NM = 21, OL = 21
x = 4, y = 6
x = 30, y = 60, z = 30
m∠1 = 90, m∠2 = 26, and m∠3 = 64
8.5
16
a = 110, b = 47
54
102
25
8
40
3
34. ∆RST ∼ ∆UVW ;
35.
36.
37.
38.
5
6
28.5
no
∆ABC ∼ ∆MNO; SSS∼
80 ft
1
ID: A
39.
40.
41.
42.
20 ft
42.3 m
7
10
43. Yes, they form a Pythagorean triple; 12 2 + 35 2 = 37 2 and 12, 35, and 37 are all nonzero whole numbers.
44. 4 3 m
45. acute
46. 9
2 ft
47. 7 2
48. 16 m
49. 5 3
50. x = 13 3 , y = 26
51. 89.12°
8
6
, cos A =
52. sin A =
10
10
53. 27.5
54. 4.8
55. 12.9
56. 11
57. 40.9
58. 7.9
59. w = 13.3, x = 10.2
60. 58
61. 37
62. 57
63. ∠1 is the angle of depression from airplane to the radar tower.
64. 39°
65. 483 in.2
66. 58.5 cm2
67. 70 in.2
8
64
68.
and
3
9
69.
70.
71.
72.
991 m 2
5 : 8; 5 : 8
5.9π cm
9.61π m2
73. 450π cm 2
74. 393.2 cm 3
75. 224π in. 3
76. 999 mm 3
2
ID: A
77. 1050 cm 3
78. 2459.9 m 3
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
4189 mm 3
no
9 : 14
3:7
100 m 2
35
67
5
66
3.5 ft
11.7
38
20.5
32.5
56
84
70
18
29
32
132
55.3
3