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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