Final Exam Review Packet
True or False:
1.______The formula for area of a kite is
2. ______If two angles are equal, they are right angles.
3. ______A trapezoid is never a parallelogram.
4. ______Two points determine one and only one plane.
5. ______8 cm is the radius of a circle with an area of 64
6. ______The sum of two acute angles is an obtuse angle.
7. ______A trapezoid may be equilateral.
8. ______Since the sum of 20°, 30°and 40° is 90°, then the angles arecomplementary.
9. ______The diagonals in a rectangle are sometimes perpendicular.
Set up and solve the following word problems.
10. Two angles are supplementary. Find the angles if one angle is 10°more than two- thirds the other angle.
11. In a triangle, B is 12° larger than A. C is equal to the sum of the first two angles. Find the angles.
12. ΔABC is isosceles and one of the base angles is 15° larger than thevertex angle. Find the angles.
Solve the following angle problems:
13. Find given:
bisectsAED
AED = 74°
BEC = 19°
______
14.Find given:
AEB = 29° 14’
CED = 31° 26’
BEC = 24° 34’
______
Draw the segment and then solve.
15. B is the midpoint of.
AC = x + 3
AB = x
16. B is between points A and C.
AB = 4x – 1
BC = 2x + 3
AC = 8x
17. Given:Circle one:Congruentor Can’t Prove
If congruent, name postulate: ______
Finish congruence statement (only if congruent):
18. Given: Circle one:Congruentor Can’t Prove
If congruent, name postulate: ______
Finish congruence statement (only if congruent):
19.Given:Circle one:Congruentor Can’t Prove
If congruent, name postulate: ______
Finish congruence statement (only if congruent):
20. Given:Circle one:Congruentor Can’t Prove
If congruent, name postulate: ______
Finish congruence statement (only if congruent):
21. Given:Circle one:Congruentor Can’t Prove
If congruent, name postulate: ______
Finish congruence statement (only if congruent):
Solve:
22. If two lines are parallel and are cut by a transversal, two alternateinterior angles represented by 3x and
5x – 70. Find the angle measures.
23. If two lines are parallel and are cut by a transversal, two corresponding angles represented by 2x + 10 and
4x -50. Find the angle measures.
Use the following sketch to solve:
24.
Find x = __________________
25. Given:.
Find:
26. Given:
bisects
Find:
= ______
______
Simplify each radical expression
27. 28. 29.
Solve the proportion.
30. 31.
Are the triangles similar? If so, write a similarity statement and identify the postulate or theorem that justifies your answer.
32. A D G
C T
O
33. Circle one:Similaror Can’t Prove
If similar, name postulate: ______
Finish similarity statement (only if similar):
34. Circle one:Similaror Can’t Prove
If similar, name postulate: ______
Finish similarity statement (only if similar):
Use the given information to determine the similar triangles. Then, solve for the missing side.
35. Given
GM = 5
AG = 6
YM = 15
Find RM = ____
36. Given find CD.
CD = ______
37. If , = 30° and = 97°, find the measures of angles Q, P, and R.
= ______
= ______
= ______
38-40. Use the diagram at the right. A, B, and C are midpoints of sides GH, HJ and GJ
respectively.
38. If and , what is AB? ______
39. If and , what is HB? ______
40. If and, what is GH? ______
41-43. Is this triangle possible?
41. 2.5, 3.5, 5 ______42. 2, 6, 9______43.______
Find the third side. Write an inequality statement.
44. 5, 15, ______
Find the missing angles.
45.
46. Find the midpointof A(4, 7) and B(-5, 8)midpoint = ______
47. Find the endpoint, B, of if A(8,-4) and the midpoint is (5, -9).B = ______
48. Find the distance between A(2,4) and B(-12, 6). Round your answer to thed = ______
nearest tenth.
49. Given the following conditional, write the converse, biconditional (if possible) and inverse statements.
If a number is divisible by two then it is even.
Converse: ______
Biconditional: ______
50. Write a proof.
Given: X is the midpoint of and.
Prove: VWX YZX
StatementReason
1. X is the midpoint of and 1. Given
2. 2. ______
3. 3. ______
4. VWX YZX4. ______
51. Write a proof.
Given: D is the midpoint of
Prove:
StatementReason
1. D is the midpoint of 1. Given
2. 2. ______
3. 3. ______
4. ADBCDB4. ______
5. 5. ______
52. Which of the triangles in the figure below must be isosceles?
a)∆SPR
b)∆SPQ
c)∆QTU
d)∆SQV
53. If the hypotenuse of a 45-45-90 triangle is 5, what is the measure of the leg?
a.b.
c.d.10
54. The length of the legs of a right triangle are 4cm and 7cm. Find the length of the hypotenuse.
a.b.
c.d.
55. Use the figure at the right to determine FG.
a.4.2b.4.7
c.9.1d.23.6
56. Find the value of x and y. Round to the nearest whole number.
a.x = 29°, y = 61°b.x = 64°, y = 26°
c.x = 26°, y = 64°d.x = 61°, y = 29°
57. If the diagonals of a quadrilateral bisect each other at right angles, the figure is a:
a. Rectangle b. Trapezoid c. Rhombusd. Kite
58. Find the following measurementsif , , , WZ = 20. WXYZ is a parallelogram.
59. Find the following measurements ifand. ABCD is a rhombus.
60. Find the following measurements in simplest radical formif . DEFG is a square.
61. A trapezoid has midsegment of 13 and one base of 21. Find the other base.
b = ______
62. A trapezoid has midsegmentof (2x+4) and bases (3x+2) and (2x+1). Solve for x.
x = ______
63. Given kite ABCD, BE = 12, BC = 20 and the and the find the indicated measures.
EC = ______
64. Find the radius. 65. Find the value of x.
r =______x =______
66. Given that the find the
67. Given that the find the
68. If the find the 69. Find a and b.
.
= ______a = ______, b = ______
70. Find the value of x.71. Find the value of x.
x = ______x = ______
72. Find the value of x.73. Find the value of x.
x = ______x = ______
74. Find x and y.
x = ______y = ______
75. Find the area and perimeter of a right triangle with a hypotenuse of 20 cm and a leg of 16 cm.
Perimeter = ______
Area = ______
76. Find the base of a parallelogram if the height is 20 cm and the area is 340 cm2.
base = ______
77. Find the height of a trapezoid if the sum of the bases is 26 ft and the area is 312 ft2.
height = ______
78. Find the area of the kite.
area = ______
79. Find the value of x, given the Area = 276 ft2.
x = ______
80. Find the value of x if the Area = 476 cm2. 81. Find the value of x if the Area = 36 in2.
x = ______x = ______
82. Find the circumference and area of the circle using the given information.
r =5 C=______A=______d=16 C=______A=______
83. Find the area of the sector of a circle if the radius is 12 m and the arc measure is 120.
a)
b)
c)
d)
84. Find the measure of the central angle if the arc length is 4ft and the radius is 16ft.
a)4
b)8
c)45
d)60
85. Find the radius of a circle if the area of one sector is 9 and the measure of the central angle is 90.
a)3
b)4
c)6
d)36
86. Find the arc length of the circle with the radius of 10 cm and central angle measure of 72.
a)12.56 cm
b)15.7 cm
c)62.8 cm
d)78.5 cm
87. Find the given the corresponding arclength 88. Find the area of sector FDE.
andthe radius. Round to the nearest tenth.Round to the nearest tenth.
area = ______
89. Find the radius given the central angle and the corresponding area of the sector( A). Round to the nearest tenth.
r = ______
90. Find the value of x.91. Find the following arc measures and label the
arcs as minor, major or semicircles.
x = ______
92. Find the sum of the measures of the interior angles of a dodecagon.
______
93. The measure of each exterior angle of a polygon is 45o. Find the number of sides of the polygon.
______
94. Find the measures of an interior and exterior angle of a regular pentadecagon.
______
95. The measure of an interior angle of a regular polygon is 120o. Find the number of sides of the polygon.
______
96. If the exterior angle of a regular polygon measures 36o, find the sum of the measures of the interior angles.
______
97. The sum of the interior angles of a polygon are 1440o. Name the polygon.
______
98. The measures of the interior angles of a pentagon are x, 3x, 2x – 1, 6x – 5, and 4x + 2. Find the measure of each angle.
______
99. P is the centroid of and and . Find the value of x.
x = ______
100. R(3,3), S(-1, 6), and T(1, 8) are the vertices of and is a median. What are the coordinates of X?
101. Find the value of x. List the sides of in order from shortest to longest for the given angle measures.
102. In which type of segment if
a.) angle bisectorb.) perpendicular bisector
c.) mediand.) altitude
103. Find the volume and surface area. 104. Find the volume and surface area.
V=______V=______
SA=______SA=______
105. Find the volume and surface area. 106. A cylinder has a volume of approximately
V=______188.4 cubic inches and a radius of 4 inches.
SA=______What is its height?
107. Find the volume and surface area. 108. Find the volume and surface area.
V=______V=______
SA=______SA=______
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