Geometry CP Name_______________________________
Fall 2014-15 Date_______________Block____________
Final Exam Review Packet
True or False:
1._______ The formula for area of a kite is 1 2.A d d
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 2 .cm
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 are complementary.
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 the vertex angle. Find the angles.
Solve the following angle problems:
13. Find ,m CED given:
EB bisects AED
mAED = 74°
mBEC = 19° m CED _________________
2
A
E D
B
C
B
I
RD
A
S N
EK
14. Find ,m AED given:
mAEB = 29° 14’
mCED = 31° 26’
mBEC = 24° 34’
m AED ____________
Draw the segment and then solve.
15. B is the midpoint of AC .
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: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
_______BID
18. Given: Circle one: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
_______SAN
AC = _____
AB = _____
BC = _____
AC = _____
AB = _____
BC = _____
3
T
A
G
O
D
C
B
A
E
B
A
C
D
19. Given: Circle one: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
_______GTA
20. Given: ADB CDB Circle one: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
_______ABD
21. Given: Circle one: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
_______ABC
Solve:
22. If two lines are parallel and are cut by a transversal, two alternate interior angles represented by 3x and
5x – 70. Find the angle measures.
4
AI
C E
F H
B
D
G
G
A
C D
F
E
B
_________
_________
m EDG
m DGH
F
BA D
E H
C
G
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. (10 8)m ABF x
(7 10)m BFH x
Find x = _____________ m EFB ___________ m CBD ____________
25. Given: 32
89
AB CE FH
m ABD
m BDG
.
Find:
26. Given: BF CD
EC bisects ACD
42m EGF
Find:
m CBF = __________
m ABG _________
5
Simplify each radical expression
27. 6004 28. 3
17 29. 542964
Solve the proportion.
30. 4
16 x
x 31.
5852
57 x
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: Similar or Can’t Prove
If similar, name postulate: ____________
Finish similarity statement (only if similar):
_______SLP
92°
92°
23°
68°
Circle one: Similar or Can’t Prove
If similar, name postulate: ____________
Finish similarity statement (only if similar):
_______CAT
6
34. Circle one: Similar or Can’t Prove
If similar, name postulate: ____________
Finish similarity statement (only if similar):
_______ABC
Use the given information to determine the similar triangles. Then, solve for the missing side.
35. Given AG YM
GM = 5
AG = 6
YM = 15
Find RM = ____
36. Given , 2 5, 4 3 and 5 6,AB DE AB CB ED find CD.
CD = ____________
7
37. If QPRABC ~ , m A = 30° and m B = 97°, find the measures of angles Q, P, and R.
m Q = ________
m P = ________
m R = ________
38-40. Use the diagram at the right. A, B, and C are midpoints of sides GH, HJ and GJ
respectively.
38. If 3 8AB x and 2 24GJ x , what is AB? __________
39. If 3 5AC y and 4 2HJ y , what is HB? __________
40. If 7 1GH x and 4 3BC x , what is GH? __________
41-43. Is this triangle possible?
41. 2.5, 3.5, 5 ___________ 42. 2, 6, 9 ___________ 43. 62,13,3 ___________
Find the third side. Write an inequality statement.
44. 5, 15, ___________________
Find the missing angles.
45.
__________
__________
__________
m CAD
m FAB
m BCA
8
46. Find the midpoint of A(4, 7) and B(-5, 8) midpoint = ____________
47. Find the endpoint, B, of ,AB 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 the d = ____________
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 VY and WZ .
Prove: VWX YZX
Statement Reason
1. X is the midpoint of VY and WZ 1. Given
2. XYVX 2. _____________________________
XZWX
3. 3. _____________________________
4. VWX YZX 4. _____________________________
9
51. Write a proof.
Given: D is the midpoint of AC
Prove: BCAB
Statement Reason
1. D is the midpoint of AC 1. Given
2. DCAD 2. _____________________________
3. BDBD 3. _____________________________
4. ADB CDB 4. _____________________________
5. BCAB 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. 5 2
2 b. 5 2
c. 5 3
3 d. 10
54. The length of the legs of a right triangle are 4 cm and 7 cm. Find the length of the hypotenuse.
a. 33 b. 2 13
c. 65 d. 2 5
10
________
________
________
________
DB
AB
ABCm
ECBm
55. Use the figure at the right to determine FG.
a. 4.2 b. 4.7
c. 9.1 d. 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. Rhombus d. Kite
58. Find the following measurements if 3 20WY x , 6 16ZX x , 108WPXm , WZ = 20. WXYZ is a
parallelogram.
__________
________
________
________
_________
WX
WYXm
WXZm
WP
x
59. Find the following measurements if 144DABm and 30AC . ABCD is a rhombus.
11
________
________
________
________
DG
EH
FHGm
DEGm
60. Find the following measurements in simplest radical form if 214DF . 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 midsegment of (2x+4) and bases (3x+2) and (2x+1). Solve for x.
x = ______________
63. Given kite ABCD, BE = 12, BC = 20 and the 105m ABC and the 85 ,m DAB find the indicated
measures.
___________m DCB
EC = ___________
64. Find the radius. 65. Find the value of x.
r =___________ x =___________
12
66. Given that the 255 ,mNQM find the .m MPN
___________m MPN
67. Given that the 55 ,m G find the .mDF
__________mDF
68. If the 60 ,mAC find the .mAB 69. Find a and b.
.
.mAB = _________ a = __________, b = __________
13
725
yx
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 = ______________
14
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 in
2.
x = ______________ x = ______________
15
_________mAB
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) 225.12 m
b) 2150.72 m
c) 2376.8 m
d) 2452.16 m
84. Find the measure of the central angle if the arc length is 4 ft 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 2m and the measure of the central angle is 90 .
a) 3 m
b) 4 m
c) 6 m
d) 36 m
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 mAB given the corresponding arc length 88. Find the area of sector FDE.
and the radius. Round to the nearest tenth. Round to the nearest tenth.
16
_________,__________
_________,__________
_________,__________
mMRQ
mPQ
mRPM
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.
____________
17
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 DEF and 82 xDP and 36 xDN . Find the value of x.
x = ________________
100. R(3,3), S(-1, 6), and T(1, 8) are the vertices of RST and RX is a median. What are the coordinates of X?
18
101. Find the value of x. List the sides of PQR in order from shortest to longest for the given angle measures.
210,593,299 xmxQmxPm
102. In FGH which type of segment if ?FJ
a.) angle bisector b.) perpendicular bisector
c.) median d.) 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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