Download Final Exam Review 1st semester Geometry

Geometry Final Exam Review
1. Based on the pattern, what are the next two terms of the sequence?
8, 17, 26, 35, . . .
2. Name the plane represented by the top of the box.
3. Using the picture above, are points D, H, and C collinear or noncollinear?
4. Using the figure to the right, what is the intersection of plane TUYX and plane VUYZ?
5. Name the ray that is opposite
H
G
F
E
Use the picture to the right for 6 and 7.
6. Name the three labeled segments that are
7. Which plane is parallel to plane EFHG?
parallel to
8. If
find the values of x, EF, and FG.
E
9.
F
G
If
and
E
10. If
, then what is the measure of
F
G
O
then what are
and
F
E
D
G
H
Use the picture at the right for 12 and 13.
11.
12.
,
N
M
bisects
diagram is not to scale.
bisects
O
L
and
Solve for x and find
,
. Find
The
. The diagram is not to scale.
13. Find the coordinates of the midpoint of the segment whose endpoints are H(10, 5) and K(8, 13).
14. Find the perimeter of the rectangle.
15. Find the circumference of the circle in terms of pi.
39 ft
40 in
78 ft
16. The figure is formed from rectangles. Find the total area.
The diagram is not to scale.
6 ft
3 ft
3 ft
9 ft
17. If the perimeter of a square is 120 in2, what is its area?
18. Identify hypothesis & conclusion of the conditional statement: If tomorrow is Monday, then yesterday was Saturday.
19. 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.
20. 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.
21.
bisects
= 7x.
22. Name an angle supplementary to
=
. Find
Complementary to AOE
C
B
A
O
D
E
23.
and
each angle.
24.
are complementary angles. m
Find m1,m3,m4
=
, and m
=
25. Line r is parallel to line t. Find m 1-7.
7 134
1 3
t
1
4 2
3
r
4
2
5
26.
. Find the measure of
6
. Find the value of x for p to be parallel to q.
3 4
5 6
1 2
p
q
27. If
and
28. Find the values of x, y, and z.
, what is
a
b
12
3 4
c
5 6
7 8
39
12
58
x z
y
29. Classify ABC by its angles, when m A = 21, m B = 84, and m C = 75.
31. Given: SRTSTR, mSRT=32, mSTU=4x.
30. Find the value of x.
Find x
S
43
x
135
R
T
U
32. 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 9-gon, one at each vertex.
33. A nonregular hexagon has five exterior angle measures of 53, 58, 67, 55, and 55. What is the measure of
the interior angle adjacent to the sixth exterior angle?
34. Given
and
, find the length of QS and TV.
35. A kite has diagonals 4.7 ft and 9 ft. What is the area of the kite?
36. DEFG is a rectangle. DF = 5x – 2 and EG = x + 38. Find the value of x and the length of each diagonal.
37. ∆ACB  ∆ ______
38. The two triangles are congruent. Find the value
B M
of the variables.
A
d
48
g
C
P
N
b
f
e
8
17
15
42
c
P
39. Justify the proof.
Given:
and
R
Q
Prove:
S
40. State whether
and
Justify your answer.
are congruent.
41. Name the angle included by the sides
N
6
&
M
6
P
44
42. 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?
21
21
43. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 58°?
44. Use the information in the figure. Find
45. Given:
,
, Find x
S
E
106
F
D
R
46. Points B, D and F are midpoints of the sides of
∆ACE. If EC=34 and DF=18, what is AC?
47. Find the value of x.
T
U
A
12
B
2x-4
F
C
D
E
48. DF bisectsEDG, find the value of x?
E
49. Find the values of the variables and the lengths
of the sides of this kite.
9x+27
y-2
x+4
F
2x+2
x+6
12x
D
30
G
Use the figure at the right for 60 and 61 ABCD is a parallelogram.
50. If mCDA= 74, then mBCD = ?
51. If mABC= 84, then mCDA=?
52. LMNO is a parallelogram. If NM = x + 41 and OL = 5x + 5
find the value of x and then find NM and OL.
D
O
N
L
M
53. For the parallelogram, if m2=3x-26 and
m4=2x-9, find m1.
3
54. Find the values of the variables in the
parallelogram?
27
4
112
y
2
z
1
55. In the parallelogram mKLO=64 and
mMLO=59, find KJM J
56. In the figure, the horizontal lines are parallel
and AB=BC=CD, find JM.
K
O
A
B
M
L 4
M
x
L
C
D
K
J
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain
57.
58. X
Y
W
Z
R
59.
and
Find
S
U
Find the area. The figure is not drawn to scale.
60.
61.
T
3 yd
3.1
3.3
17 yd
62. The area of parallelogram is 80cm2 and the height is 20cm. What is the base?
63. Find the value of x
15
x
10
8
Find the length of the missing sides. The triangle is not drawn to scale.
64.
65.
10
7
24
8
66. A triangle has sides of lengths 10,24 and 26. Classify the triangle by angles.
67. A regular hexagon has a perimeter of 60 m. Find its area. Leave your answer in simplest radical form.
Find all the missing sides.
68.
69.
70.
45
10
15
45
30
28
71. Write the standard equation for the circle with center at (6,5) and radius 4.
72. Find the center and radius of the circle with equation (x – 9) + (y + 10) = 100
Find the missing angle measures
73.
74.
75.
20
21
4
15
8
35
Find the circumference and area. Leave your answer in terms of
76.
77.
.
X
4.6
10
8
P
Y
78. Find the length of arc XPY. Leave your answer in terms of
79. The circumference of a circle is 46
cm. Find the diameter, the radius, and the length of an arc of 160°
80. Find the area of a sector with a central angle of 190° and a diameter of 7.9 cm. Round to nearest 10 th.
81. 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?
82. On a blueprint, the scale indicates that 4 cm represent 18 feet. What is the length of a room that is 7.2 cm
B
long and 6 cm wide on the blueprint?
X
83. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 50. Find YZ. The
figures are not drawn to scale.
W
Y
C
A
Z
84. Explain why the triangles are similar. Then find the value of x.
D
)
x
12
)
27
21
Find the geometric mean
of the
pair of numbers.
Not drawn
to scale
85. 169 and 4
86. 3 and 7
Solve for the variables.
87.
88.
6.8
x
z
x
5.4
y
17.5
5
4
89. The widths of two similar rectangles are 24 m and 27 m. What is the ratio of the perimeters? Of the areas?
90. Find the volume and surface area of a sphere with radius of 5 mm.
Find the values of each variable.
91.
92.
93. x
50
65
y
y
x
8
y
8
94.
95.
96.
z
z
y
16
x
x
z
9
15
10
x
24
z
z
z
x
22
y
20
y
14
Use formulas to find the volume of the given prism
97.
98.
9m
5m
99.
9m
100.
9 cm
20 m
3m
1m
19 m
35 m
18 cm
8m
Find the volume for each figure.
101.
102.
15 cm
5 yd
3 cm
6 yd
6 yd
Assume that lines that appear to be tangent are tangent. Find the value of the variable.
103.
29
104.
x
25
x
31
In the figure,
and
are tangent to circle O and
105.
For mAOC = 40, find mPOB.
106.
For mAOC = 51, find mBPO.
10
bisects
.
D
B
O
C
A
P
Assume that lines that appear to be tangent are tangent. Find the value of the variable.
107.
108.
109.
x
x
34
x
8
110.
24
6
111.
112.
x
x
8
8
O
7
x
40
22
36
113.
and
of YXR.
are diameters. Find the measure
Y
.
Z
72
X
48 C
114. m(arc DE) = 103 and m(arc BC) = 47. Find
m A.
A
R
B
D
C
E
W