Download Final Exam Review 1st semester Geometry

Final Exam Review
Geometry
Name________________
1. Based on the pattern, what are the next two terms of the sequence?
8, 17, 26, 35, . . .
2. Based on the pattern, make a conjecture about the sum of the first 30 positive even numbers.
2
=
2 =
2+4
=
6 =
2+4+6
= 12 =
2+4+6+8
= 20 =
2 + 4 + 6 + 8 + 10
= 30 =
3. Name the plane represented by the top of the box.
4. Using the picture above, are points D, H, and C collinear or noncollinear?
5. What is the intersection of plane TUYX and plane VUYZ?
6. Name the ray that is opposite
G
E
H
F
Use the following picture for 7 and 8.
7. Name the three labeled segments that are parallel to
9. If
E
8. Which plane is parallel to plane EFHG?
find the values of x, EF, and FG.
F
G
10. If
and
E
, then what is the measure of
F
G
O
11. If
then what are
and
The diagram is not to scale.
F
E
D
G
H
L
O
N
Use the picture at the right for 12 and 13.
M
12.
bisects
diagram is not to scale.
13.
bisects
and
,
Solve for x and find
,
. Find
The
. The diagram is not to scale.
14. Find the coordinates of the midpoint of the segment whose endpoints are H(10, 5) and K(8, 13).
15. Find the perimeter of the rectangle.
16. Find the circumference of the circle in terms of .
40 in
39 ft
78 ft
17. The figure is formed from rectangles. Find the total area. The diagram is not to scale.
3 ft
6 ft
3 ft
9 ft
18. If the perimeter of a square is 120 inches, what is its area?
19. Identify the hypothesis and conclusion of this conditional statement:
If tomorrow is Monday, then yesterday was Saturday.
20. For the following true conditional statement, write the converse. If the converse is also true, combine the
statements as a biconditional.
If x = 9, then x2 = 81.
21. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are supplementary, then the sum of their measures is 180°.
and
are supplementary.
Name the Property of Equality or Congruence that justifies the statement:
22. If x = y, then
.
23. If
24. If
.
.
25.
bisects
= 7x.
= 3x + 3. Find
26. Name an angle supplementary to
C
B
A
O
D
E
27.
angle.
and
28.
are complementary angles. m
Find
29.
=
, and m
1
2
3
7 134
1 3
r
4
2
5
30.
. Find the measure of each
Line r is parallel to line t. Find m 5.
t
4
=
6
. Find the value of x for p to be parallel to q.
3 4
5 6
1 2
p
q
31. If
and
a
c
b
12
3 4
, what is
32. Find the values of x, y, and z.
39
5 6
7 8
58
12
x z
y
33. Classify ABC by its angles, when m A = 21°, m B = 84°, and m C = 75°.
34. The triangular playground has angles whose measures are in the ratio 4 : 9 : 2. What is the measure of the
smallest angle?
36. Given: SRTSTR, mSRT=32, mSTU=4x. Find x
35. Find the value of x.
S
43
135
x
R
T
U
37. Use less than, equal to, or greater than to complete the statement. The sum of the measures of the exterior
angles of a regular 8-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 9gon, one at each vertex.
38.
39. The two triangles are congruent. Find the value of d.
M C
N
d
48
g
P A
f
B
40. Given
and
41. State whether
and
Justify your answer.
6
are congruent.
17
b
42
e
8
15
c
, find the length of QS and TV.
42. Name the angle included by the sides
N
and
M
6
P
43. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 44° and the two
congruent sides each measure 21 units?
44
21
21
44. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 58°?
45. Use the information in the figure. Find
E
46. Given:
Find x
,
S
106
F
D
R
47. Points B, D, and F are midpoints of the sides
of
EC = 34 and DF = 18. Find AC.
48. Find the value of x.
A
B
12
F
C
E
D
2x-4
T
U
49.
bisects
Find the value of x.
50. What is the name of the segment inside the large triangle?
E
9x+27
F
12x
30
D
G
51. What is the contrapositive of this statement?
If you have sea water, you can make salt.
52. Find the values of the variables and the lengths of the sides of this kite.
y-2
x+4
2x+2
x+6
A
B
Use the figure at the right for 53 and 54 ABCD is a parallelogram.
C
D
53. If
then
54. If
then
55. LMNO is a parallelogram. If NM = x + 41 and OL = 5x + 5 find the value of x and then find NM and OL.
N
O
L
M
56. For the parallelogram, if
and
find
3
57. Find the values of the variables in the parallelogram.
2
112
z
x
y
1
58. In the parallelogram,
Find
J
and
59. In the figure, the horizontal lines are parallel
and
Find JM.
A
M
K
O
M
27
4
L4
B
K
C
J
D
L
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain
Y
60.
61. X
N
W
Z
62. DEFG is a rectangle. DF = 5x – 2 and EG = x + 38. Find the value of x and the length of each diagonal.
R
63.
and
Find
The diagram is not to scale.
S
U
Find the area. The figure is not drawn to scale.
64.
65.
T
3.1
3 yd
17 yd
3.3
66. The area of a parallelogram is 80 cm2 and the height is 20 cm. Find the corresponding base.
Find the length of the missing side. The triangle is not drawn to scale.
67.
68.
10
7
8
24
69. A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain.
For questions 70 – 75, find the measures of the missing sides.
70.
71.
72.
45
15
28
30
10
45
73.
74.
60
15
75.
30
21
8
60
76.
77.
78.
79.
A piece of art is in the shape of an equilateral triangle with sides of 5 in. Find the area of the piece of art.
A kite has diagonals 4.7 ft and 9 ft. What is the area of the kite?
The area of a regular hexagon is 45in.2. Find the length of a side. Round your answer to the nearest tenth.
A regular hexagon has a perimeter of 60 m. Find its area. Leave your answer in simplest radical form.
Find the circumference and area. Leave your answer in terms of .
80.
81.
10
4.6
82. The circumference of a circle is 46 cm. Find the length of the diameter and the area of the circle.
83. A model is made of a car. The car is 4 meters long and the model is 3 centimeters long. What is the
ratio of the length of the car to the length of the model?
84. On a blueprint, the scale indicates that 4 cm represent 18 feet. What is the length of a room that is 7.2
cm long and 6 cm wide on the blueprint?
85. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 50. Find YZ. The figures are not drawn to scale.
B
X
W
Y
C
A
Z
D
86. Explain why the triangles are similar. Then find the value of x.
)
x
12
)
27
21
Not drawn to scale
Find the geometric mean of the pair of numbers.
87. 169 and 4
88. 3 and 7
Solve for the variables.
89.
90.
6.8
x
z
x
5.4
y
17.5
5
4
91. The widths of two similar rectangles are 24 m and 27 m. What is the ratio of the perimeters? Of the areas?
Find the value of the variables. Round your answer to the nearest tenth.
92.
93.
94.
65
y
8
x
50
x
y
z
y
8
z
z
x
15
10
95.
96.
24
97.
z
y
x
z
16
z
9
20
x
x
y
22
y
14
Use formulas to find the volume of the given prism.
9m
98.
9m
99.
1m
19 m
3m
35 m
8m
100.
101.
5m
9 cm
20 m
18 cm
102. The radius of the base of a cylinder is 37 mm and its height is 51 mm. Find the volume of the cylinder in
terms of .
Find the volume for the figures shown to the nearest whole number.
103.
104.
5 yd
15 cm
6 yd
3 cm
6 yd
105. Write the standard equation for the circle that has a center at (6, -5) and a radius of 5 meters.
106. Find the center and radius of the circle with equation (x – 9) + (y + 10) = 100.
Assume that lines that appear to be tangent are tangent. Find the value of the variable.
107.
108.
x
x
8
109.
24
6
110.
8
111.
x
8
x
O
7
x
22
36
40