GEOMETRY - Neshaminy School District
GEOMETRY
FINAL EXAM REVIEW
I. MATCHING
__C__reflexive a. a(b + c) = ab + ac
__B__transitive b. If a = b & b = c, then a = c.
__D__symmetric c. a = a
__E__substitution d. If a = b, then b = a.
__A__distributive e. If a + b = c and a = d, then
d + b = c.
II. Fill in the blank.
1. An equilateral triangle is also a(n) ____equiangular_____triangle.
2. The __hypotenuse_____ is the longest side of a right triangle.
3. Similar triangles have congruent corresponding __angles_______ and the corresponding __sides____ are in proportion.
4. In an isosceles triangle, the __vertex_____ angle is the angle that is different.
5. The __median____ of a triangle is a segment from a vertex to the midpoint of the opposite side.
6. A(n) __altitude_____ of a triangle is a segment from a vertex ( to the opposite side.
7. A(n) __perpendicular____ ___bisector_____ of a segment is a line, segment, or ray ( to a segment at its midpoint.
8. Congruent circles are circles with the same ___radius______.
9. The measure of a central angle is ___congruent___ to its intercepted arc.
10. Two ___complementary_____ angles have a sum of 90(.
11. Two ___supplementary______ angles have a sum of 180(.
12. A ___ray_____ has only 1 endpoint.
13. If two lines are ___perpendicular____, they form right angles.
14. Two lines intersect in a ___point_________.
15. Two planes intersect in a ___line_________.
16. A plane and a line not on that plane intersect in a ___point_______.
17. __Acute________ angles measure between 0( and 90(.
18. __Obtuse_______ angles measure between 90( and 180(.
19. The area of a square whose side is 4 is ___16 units2_____.
20. If the ratio of the measures of the angles of a triangle is 2:2:5, then the triangle is a(n) ____isosceles_____ triangle.
21. A rhombus whose side is 4 inches has one angle of 60(. The longer diagonal is __4[pic]_____.
22. If 4 points all lie on the same line, then the points are ___collinear______.
23. The interior angle sum of a hexagon is ___720°_______.
24. The exterior angle sum of a decagon is ___360°_______.
25. If each interior angle of a regular polygon is 144, then the polygon is a __decagon______.
26. If each exterior angle of a regular polygon is 30, then the polygon has ___12______ sides.
27. In a 30( - 60( - 90( triangle, the long leg is __[pic]__ times the short leg.
28. In a 45( - 45( - 90( triangle, the hypotenuse is __[pic]___ times the leg.
29. An angle inscribed in a semicircle is a __right_____ angle.
30. Write [pic] in simplest radical form. __4[pic]___
31. The geometric mean between 4 and 9 is ___6____.
32. If [pic]A is a right angle and m[pic]A = 4x + 10, then x = ___20_____.
33. [pic]3 & [pic]5 are _same-side interior_ angles & therefore are _supplementary.
34. [pic]4 & [pic]5 are _alternate-interior_ angles & therefore are __congruent__.
35. [pic]2 & [pic]6 are _corresponding_ angles & therefore are __congruent_____.
36. If m[pic]6 is twice the m[pic]4, then m[pic]6 =__120___.
37. True or False. A triangle may have sides of 7, 12, and 18.
TRUE; 7 + 12 > 18
38. Every triangle must have __three______ altitudes.
39. To find the area of a right triangle, the ___legs_____ can be used as the base and height.
40. A __circle_________is the set of points in a plane at a given distance from a given point in that plane.
41. A __sphere________ is the set of points in space at a given distance from a given point.
42. [pic] is a ___radius_____.
43. [pic] is a ___diameter___.
44. [pic] is a ____chord_____.
45. [pic] is a ____secant_____.
46. [pic] is a ____tangent____.
47. Point O is the ___center__________.
48. Point A is the __point of tangency____.
49. x = __20___
50. m[pic]ABD = __70___
3x + 10 + 4x + 4x – 50 = 180
11x – 40 = 180
11x = 220
x = 20
51. x = __6___
[pic]
52. B & E are the midpoints of AD and AG.
If DG = 40, then CF __30___.
53. Find the perimeter of a right triangle with legs 6 and 8. __24 units___
54. If the diagonals of a rhombus are 20 and 36, then the area is _360 units2_.
55. Find the area of a right triangle whose hypotenuse is 25 and whose leg is 7. ___84_units2___
Name the theorem or postulate used to prove the triangles congruent.
56. ___SAS_____ 57. ___ASA_____
58. ___AAS or HL___ 59. ___SSS_____
60. m[pic] = _50[pic]_
61. m[pic] =_50[pic]_
62. m[pic]COB = _50[pic]_
63. m[pic]AOB = _180[pic]_
64. Draw [pic]ACB. m[pic]ACB = __90[pic]__
65. ZY = __8 ft__
66. m[pic]Z = __60[pic]___
67. Draw altitude ZW.
68. WY = __4 ft__
69. ZW = __4[pic] ft_
70. Area of Circle = __25[pic] units2__
71. Area of Square = __100 units2___
72. Area of shaded region = __(100 – 25[pic]) units2__
73. Circumference of Circle = __10[pic] units__
74. Perimeter of Square = __40 units__
75. Area of parallelogram = _120[pic] units2__
Round your answer to the nearest whole number or degree.
76. Find y ( ___28______.
77. Find x [pic] ___57[pic]_____.
78. A ladder is positioned against a house at a 65( angle. The ladder is 10
feet tall. How far away from the house is the base of the ladder? Round
your answer to the nearest tenth.
____4.2 ft______
79. x = __75__
80. y = __75__
81. z = __30__
82. x = __3__
83. 2 tangent lines drawn to a circle from the same point are __congruent___.
84. m[pic]C = __70__
85. m[pic]A = _40__
86. Draw in altitude CD.
87. m[pic]BDC = __90__
88. m[pic]BCD = __20__
89. m[pic]ACD = __50__
90. Given: m[pic]ADC = 90(
DB = __8___
AD = __8[pic]__
DC = __4[pic]__
91. If the diagonals of a quadrilateral are (, then the quad. is a __rhombus____.
92. If the diagonals of a quad. are ( and (, then the quad. is a ___square______.
93. If the diagonals of a quad. are (, then the quad. is a _square__________ or a
___rectangle__________.
94. The bases of a trapezoid are 10 and 20. The length of the median is __15__.
95. In a parallelogram, __same-side interior______ angles are supplementary and
__opposite________ angles are congruent.
96. Given ∆XYZ ( ∆RSN, then [pic]Y ( _[pic]S__ and [pic]( __[pic]___.
97. x = _70__
O is the center & [pic] is tangent to Circle O.
98. XZ = 9, YZ = 4, WX = _3[pic]___
99. m[pic] = 100(, m[pic] = 90(, m[pic]X = _35__
100. [pic] is a __minor____ arc.
101. [pic] is a __major____ arc.
102. Find the volume of the figure above. ___72 units3__________
Leave your answers in terms of [pic].
103. Find the total surface area for the figure below.
56[pic] units2
104. What is the lateral area of a cylinder whose height is 3 and radius is 4?
24[pic] units2
105. What is the volume of the cylinder?
48[pic] units3
106. What is the volume of a cone whose radius is 9 and slant height is 13?
54[pic][pic] units3
107. The surface area of a sphere is 64[pic]. Find the radius of the sphere.
4 units
108. Find m[pic]BCD.
75
109. Given: AB = CD
Prove: AC = BD
Statements Reasons
1. AB = CD 1. Given
2. BC = BC 2. Reflexive Property
3. AB + BC = BC + CD 3. Addition Property of Equality
4. AC = AB + BC; BD = BC + CD 4. Segment Addition Postulate
5. AC = BD 5. Substitution Property
110. Given: Y is the midpoint of [pic] and [pic].
Prove: [pic]W [pic] [pic]V
Statements Reasons
1. Y is the midpoint of [pic] and [pic] 1. Given
2. [pic] [pic] [pic]; [pic][pic] [pic] 2. Definition of midpoint
3. [pic]XYW [pic][pic]ZYV 3. Vertical angles are congruent
4. [pic]XYW [pic][pic]ZYV 4. SAS Postulate
5. [pic]W [pic] [pic]V 5 CPCTC
111. XZ = 16, WY = 4. Find the area of [pic]WXZ.
32 units2
112. Find the ratio of the perimeter of a square with length 4 inches to the perimeter of a square with length 6 inches.
2 : 3
113. Find CD.
6
10
114. List the sides from largest to smallest.
[pic], [pic], [pic]
115. Points A, B, and C are collinear. If AC = 8, BC = 6, and AB = 14, which point is in between the other two? ___C________
116. OA = 8 and m[pic]AOB = 90. Find AB.
[pic]
117. In [pic]O, the radius is 41, and XZ = 18, find OM.
40
118. In [pic]ABC, AB = BC, m[pic]A = 32[pic], and BD is an altitude. Find m[pic]CBD.
58[pic]
119. If a quadrilateral is inscribed in a circle then opposite angles are ____supplementary_______.
120. Find the scale factor if the perimeters of two rectangles are 36 cm and 48 cm respectively.
[pic]
121. List the sides of [pic] from smallest to largest.
[pic], [pic], [pic][pic]
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