Name: Mod: Geometry Mrs. Crocker Spring 2014 Final Exam Review Use this exam review to complete your flip book and to study for your upcoming exam. You must bring with you to the exam: 1. Pencil, eraser, and calculator 2. Flip Book You may bring with you to the exam: 1. A handwritten 3x5 notecard with important formulas (both sides may be used) 2. This exam review (at least 50% complete) for extra credit on the exam Your exam will consist of two parts: Multiple Choice and Free Response covering the following chapters Chapter 6: Polygons and Quadrilaterals Chapter 7: Similarity Chapter 8: Trigonometry and Right Triangles Chapter 9: Transformations Chapter 10: Area Chapter 11: Surface Area and Volume Chapter 12: Circles Mod 5-6: Tuesday 6/3 9:35-11:35 Mod 14-15: Monday 6/2 12:25-2:25
Chapter 6 - Polygons & Quadrilaterals In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: A. Angle-Sum Theorem B. Exterior Angle-Sum Theorem C. Properties of Parallelograms D. Rhombus, Rectangle, Square E. Trapezoid & Kite F. Midsegment of Trapezoid Solve the following problems to practice these above concepts. Use a pencil and show work. 1. What is the sum of the angle 2. What is the sum of the angle measures of a hexagon? measures of an 18-gon? For #3 & 4, find the measure of one interior angle of the following regular polygons: 3. 72-gon 4. Pentagon For #5 & 6, find the measure of one exterior angle of the following regular polygons: 5. 36-gon 6. Octagon For #7 & 8, find the value of x. 7. 8. List the five properties of parallelograms (notes 6.2): 9. 10. 11. 12. 13.
For #14 & 15, use the properties of parallelograms to find the value of the variable(s). 14. 15. For #16 & 17, what values of x make each figure the given special parallelogram? 16. rhombus 17. Rectangle For #20 22, decide whether the parallelogram is a rhombus, rectangle, or square. Explain. 18. 19. 20. 21. For #22 & 23, find x given the midsegment of the trapezoid. 22. 23. Find the values of the variables of the kite: 24.
Chapter 7 - Similarity In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: G. Similar Polygons H. Proving Triangles are Similar I. Similarity in Right Triangles J. Proportions in Triangles Solve the following problems to practice these above concepts. Use a pencil and show work. 25. Two angles are complementary and in the ratio 1 : 4. What are the degree measures of each of the angles? 26. The measures of the angles of a triangle are in the extended ratio 4 : 6 : 10. What are the measures of each of the angles? Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used. If not, explain. 27. 28. 29. Find the value of z. Give the scale factor of the polygons.
For #30 35, use the diagram at the right, 30. The scale factor of 31.. Find each of the following. 32. 33. 34. 35. For #36 39, solve for and. 36. 37. 38. 39. 40. 41. For #42 & 43, find the geometric mean for each pair of numbers. 42. 43.
Chapter 8 - Trigonometry & Right Triangles In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: K. Converse of the Pythagorean Theorem L. and Triangles M. Trig Functions N. Angles of Depression and Elevation Solve the following problems to practice these above concepts. Use a pencil and show work. For #44 46, the lengths of the sides of a triangle are given. Classify the triangle as acute, right, or obtuse. Show work. 44. 15, 8, 17 45. 4, 9, 11 46. 5, 6, 7 For #47 & 48, find the value of each variable: 47. y = 48. x = For #49 56, find the value of each variable. 49. 50. 51. 52. 53. 54.
55. 56. For #57 60, describe each angle (elevation or depression) as it relates to the situation in the diagram. 27. 28. 29. 60. 61. An eagle perched 40 ft up in a tree looks down at a angle and spots a vole. How far is the vole from the eagle to the nearest tenth of a foot? Draw and label a diagram. 62. A person is standing 40 ft from a flagpole and can see the top of the pole at a angle of elevation. The person s eye level is 4 ft from the ground. What is the height of the flagpole to the nearest foot? Draw and label a diagram.
Chapter 9 - Transformations In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: O. Transformations Solve the following problems to practice these above concepts. Use a pencil and show work. 63. Define an isometry: For #64 & 65, graph the image of each figure under the given translation. 64. ( ) ( ) 65. ( ) ( ) For $66 & 67, the dashed-line figure is a translation image of the solid-line figure. Write a rule to describe each translation. 66. 67. Each point is reflected across the line indicated. Find the coordinates of each image. 68. A across the y-axis: 69. B across the x-axis: 70. C across y = -1: 71. D across x = -1: 72. E across x = -3:
For #73 & 74, given points M(-1, 3), N(2, -2), and O(3, 1), graph and its reflection image across the line and apply a dilation with center (0,0) and scale factor 2. 73. x = 2 74. Dilate with scale factor of 2 For #75 78, tell what type(s) of symmetry each figure has. It if has line symmetry, sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation. 75. 76. 77. Regular 78. Regular Pentagon Hexagon The dashed-line figure is a dilation image of the solid-line figure. The labeled point is the center. Tell whether the dilation is an enlargement or a reuction. Then find the scale factor. 79. 80.
Chapter 10 - Area In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: P. Area of Parallelograms & Triangles Q. Area of Trapezoids R. Area of Rhombuses & Kites S. Area of Regular Polygons T. Perimeter & Area of Similar Figures Solve the following problems to practice these above concepts. Use a pencil and show work. For #81 88, find the area of each figure. Round to the nearest tenth if necessary. 81. 82. 83. 84. 85. 86. 87. 88.
For #89 & 90, find the area of each composite shape. 89. 90. For #91 & 92, find the measure of each numbered angle: 91. 92. For #93 & 94, the figures in each pair are similar. What are the ratio of the perimeters and the ratio of the areas? 93. 94. 95. The areas of two similar triangles are 25 m 2 and 49 m 2. Find their scale factor.
Chapter 11 - Surface Area & Volume In your flip books complete the following topics. Write necessary formulas, information, and draw diagrams: U. Surface Area of Prisms & Cylinders V. Surface Area of Pyramids & Cones W. Volume of Prisms & Cylinders X. Volume of Pyramids & Cones Y. Spheres Solve the following problems to practice these above concepts. Use a pencil and show work. For #96 101, find the surface area of each. Round to the nearest tenth if necessary. 96. 97. 98. 99. 100. 101. For #102 107, find the volume of each. Round to the nearest tenth if necessary. 102. 103.
104. 105. 106. 107. For #108 & 109, find the surface area and volume of each sphere. Leave answers in terms of. 108. 109. Find the surface area and volume of the composite shape. Leave answers in terms fo. 110.
Chapter 12 - Circles (also 10.6 & 10.7) In your flip books complete the following topics. Write necessary formulas, draw diagrams: information, and Z. Arc Length AA. Area of Sector BB. Tangent Lines CC. Chords & Arcs DD. Inscribed Angles Solve the following problems to practice these above concepts. Use a pencil and show work. 111. Name a minor arc: 112. Name a major arc: 113. Name a semicircle: Find the measure of each arc in. 114. : 115. : 116. : 117. : 118. : 119. : For #120 & 121, find the length of the darkened arc. Round answer to the nearest tenth. 120. 121. For #122 125, find the area of the shaded region. Round answers to the nearest tenth. 122. 123. 124. 125.
For #126 133, all lines that appear tangent are tangent. Find the value of the variable(s). 126. 127. 128. 129. 130. 131. 132. 133. Determine whether a tangent line is shown. 132.