Geometry CP
Name_______________________________
Date_______________Block____________
Final Exam Review Packet
True or False:
1._______ The formula for area of a kite is A  d1d2 .
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  cm 2 .
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
m AED = 74°
m BEC = 19°
mCED  _________________
A
B
14. Find mAED, given:
m AEB = 29° 14’
m CED = 31° 26’
m BEC = 24° 34’
mAED  ____________
C
E
D
Draw the segment and then solve.
15. B is the midpoint of AC .
AC = x + 3
AB = x
AC = _____
AB = _____
BC = _____
16.
AC = _____
AB = _____
BC = _____
B is between points A and C.
AB = 4x – 1
BC = 2x + 3
AC = 8x
I
17. Given:
Circle one: Congruent or Can’t Prove
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
BID   _______
B
R
D
S
N
Circle one: Congruent or Can’t Prove
18. Given:
If congruent, name postulate: ______________
A
Finish congruence statement (only if congruent):
2
E
K
SAN   _______
G
19. Given:
Circle one: Congruent or Can’t Prove
O
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
GTA   _______
T
A
20. Given: ADB  CDB
Circle one: Congruent or Can’t Prove
A
If congruent, name postulate: ______________
Finish congruence statement (only if congruent):
ABD   _______
B
D
C
D
Circle one: Congruent or Can’t Prove
21. Given:
If congruent, name postulate: ______________
A
Finish congruence statement (only if congruent):
C
ABC   _______
E
B
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.
3
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.
C
Use the following sketch to solve:
A
B
E
F
D
H
G
24. mABF  (10 x  8)
mBFH  (7 x  10)
Find x = _____________
AB CE FH
25. Given: mABD  32 .
mBDG  89
Find:
mEDG  _________
mDGH  _________
mEFB  ___________ mCBD  ____________
A
B
E
D
C
I
G
F
H
A
E
26. Given: BF CD
EC bisects ACD
mEGF  42
B
Find:
G
F
mCBF = __________
mABG  _________
C
4
D
Simplify each radical expression
4 600
27.
28.
17
3
29.
4 96  2 54
Solve the proportion.
16 x

30.
x 4
7 5
x

2 5 8 5
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
92°
C
68°
23°
Circle one: Similar or Can’t Prove
T
92°
If similar, name postulate: ____________
O
Finish similarity statement (only if similar):
CAT
 _______
Circle one: Similar or Can’t Prove
33.
If similar, name postulate: ____________
Finish similarity statement (only if similar):
SLP
5
 _______
Circle one: Similar or Can’t Prove
34.
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 AB DE , AB  2 5, CB  4 3 and ED  5 6, find CD.
CD = ____________
6
37. If ABC ~ QPR , 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 AB  3x  8 and GJ  2x  24 , what is AB? __________
39. If AC  3 y  5 and HJ  4 y  2 , what is HB? __________
40. If GH  7 x 1 and BC  4x  3 , what is GH? __________
41-43. Is this triangle possible?
41. 2.5, 3.5, 5 ___________
42. 2, 6, 9 ___________
43.
3 , 13 ,2 6 ___________
Find the third side. Write an inequality statement.
44. 5, 15, ___________________
Find the missing angles.
45.
mCAD  __________
mFAB  __________
mBCA  __________
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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
nearest tenth.
d = ____________
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
1. X is the midpoint of VY and WZ
Reason
1. Given
2. VX  XY
2. _____________________________
WX  XZ
3. ∠𝑊𝑋𝑉 ≅ ∠𝑌𝑋𝑍
3. _____________________________
VWX ≅ ∆YZX
4. _____________________________
4.
8
51. Write a proof.
Given: D is the midpoint of AC
∠𝐴𝐷𝐵 ≅ ∠𝐵𝐷𝐶
Prove: AB  BC
Statement
1. D is the midpoint of AC
Reason
1. Given
∠𝐴𝐷𝐵 ≅ ∠𝐵𝐷𝐶
2. AD  DC
2. _____________________________
3. BD  BD
3. _____________________________
4.
ADB ≅ ∆CDB
5. AB  BC
4. _____________________________
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.
c.
5 2
2
5 3
3
b.
5 2
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
9
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 WY  3x  20 , ZX  6x 16 , mWPX  108 , WZ = 20. WXYZ is a
parallelogram.
x  _________
WP  ________
mWXZ  ________
mWYX  ________
WX  __________
59. Find the following measurements if mDAB  144 and AC  30 . ABCD is a rhombus.
mECB  ________
mABC  ________
AB  ________
DB  ________
10
60. Find the following measurements in simplest radical form if DF  14 2 . DEFG is a square.
mDEG  ________
mFHG  ________
EH  ________
DG  ________
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 mABC  105 and the mDAB  85, find the indicated
measures.
mDCB  ___________
EC = ___________
64. Find the radius.
65. Find the value of x.
r =___________
x =___________
11
66. Given that the mNQM  255, find the mMPN.
mMPN  ___________
67. Given that the mG  55, find the mDF .
mDF  __________
68. If the mAC  60, find the mAB.
69. Find a and b.
.
mAB. = _________
a = __________, b = __________
12
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.
25
7
x
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 = ______________
13
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 = ______________
14
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 4  ft and the radius is 16ft.
a)
b)
c)
d)
85.
25.12 m 2
150.72 m2
376.8 m2
452.16 m 2
4
8
45 
60 
Find the radius of a circle if the area of one sector is 9  m 2 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 m AB given the corresponding arc length
and the radius. Round to the nearest tenth.
mAB  _________
88. Find the area of sector FDE.
Round to the nearest tenth.
area = __________
15
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.
mMRQ  _________, __________
x = ______________
mPQ  _________, __________
mRPM  _________, __________
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.
____________
16
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 DP  2x  8 and DN  6x  3 . 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?
17
101. Find the value of x. List the sides of PQR in order from shortest to longest for the given angle
measures.
mP  9 x  29, mQ  93  5 x, m10 x  2
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.
V=_________
SA=_________
104. Find the volume and surface area.
V=_________
SA=_________
105. Find the volume and surface area.
V=_________
SA=_________
106. A cylinder has a volume of approximately
188.4 cubic inches and a radius of 4 inches.
What is its height?
107. Find the volume and surface area.
V=_________
SA=_________
108. Find the volume and surface area.
V=_________
SA=_________
18