Second Semester Exam Review Packet
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1 Geometry Name Second Semester Exam Review Packet CHAPTER 7 THE PYTHAGOREAN THEOREM. This theorem is used to find the lengths of the sides of a right triangle. Label the parts of the right triangle. What does the Pythagorean Theorem say about the relationship of the parts of a right triangle? 1. a represents a of the triangle. 2. b represents a of the triangle. 3. c represents the of the triangle. 4. If a 2 + b 2 = c 2 then the triangle is a triangle. 5. If a 2 + b 2 < c 2 then the triangle is an triangle. 6. If a 2 + b 2 > c 2 then the triangle is an triangle. 7. Determine if a triangle with sides 26, 35, 60 is an acute, right, or obtuse triangle. 8. Determine if a triangle with sides 27, 36, 45 is an acute, right, or obtuse triangle. 9. One leg of a right triangle is 6 inches and the other is 6 3. Find the length of the hypotenuse. 10. What are the special right triangle relationships? 11. Find the exact value of x. 12. Find the exact value of x Find the exact value of x. 14. Find the exact value of x. 15. Find the exact values of x and y.
2 16. The geometric mean of 2 #s is the number x that satisfies a x = x b such that ab = x 2. In the figure, the following are geometric means: BD (the altitude) is the geometric mean between and AB (left leg) is the geometric mean between and BC (right leg) is the geometric mean between and 17. Solve for the exact value of n. 18. Solve for the exact value of k is the geometric mean of 9 and what number? Trigonometric Ratios: Name Abbreviation Ratio of sides A Sine sin 20. sin(a) = leg Cosine cos 21. cos(a) = adjacent to A Tangent tan C 22. tan(a) = 23. What does it mean to solve a right triangle? hypotenuse leg opposite of A B 24. Solve the right triangle. 25. Solve the right triangle. 26. Solve the right triangle. 27. From the top of a 200 foot cliff, John sees a sailboat at an angle of depression of 47. How far is the sailboat from the base of the cliff? 28. Sarah stands 110 meters from the base of a water tower. She measures the angle of elevation to the top of the tower to be 62. How tall is the tower?
3 CHAPTER What is the FORMULA for sum of the interior angles of ANY convex polygon? 30. What is the SUM of the exterior angles of ANY convex polygon? 31. What is the relationship between one interior angle and its exterior angle? 32. What is the sum of the interior angles of the given regular pentagon? 33. What is the measure of each interior angle if it is a regular polygon? 34. What is the sum of the measures of the exterior angles? 35. What is the measure of each exterior angle? 36. Find x. 37. The sum of the measures of the interior angles of a convex polygon is 8640!. How many sides does the polygon have? 38. Find the sum of the interior angles of a convex 20-gon 39. Each interior angle of the regular n-gon has a measure of 165º. How many sides does the n- gon have? 40. Find the measure of one interior angle and one exterior angle of a regular decagon.
4 41. What are the 5 common properties of all parallelograms? 42. What additional properties do squares have? 43. What additional properties do rectangles have? 44. What additional properties do rhombi have? 45. Draw rhombus ABCD with the diagonals intersecting at point E. If!ABC = 120 " and EC = 12 find the following. 46. Draw rectangle QUAD and its diagonals. If QA = x 2! 2x + 4 and DU = 12 find x. a) m!bce b) m!bec c) AD d) DE 47. If DB = 12 Find AC. 48. QRST is a rectangle. QZRC is a parallelogram.!tqc = 70 ". Find m!rcs, m!rts, and m!qzr. If QC = x 2! 18 and TC =!7x, find ZR.
5 CHAPTER A central angle 50. An Angle INSIDE the circle 51. An angle OUTSIDE the circle 52. An angle ON the circle 53. Chords intersecting inside the circle 54. Segments outside the circle 55. Solve for x. 56. Solve for x. 57. Solve for x. 100 x 58. Solve for x. 59. Solve for x. 60. Solve for x. x 6 8 x Solve for x. 62. Solve for x. 63. The diameter of the circle is 10. Find the length of the other chord Write the equation of a circle with center (3, -5) and diameter State the center and radius of a circle with equation ( x + 11) 2 + y 2 = Write the equation of a circle whose center is (2, 4), given that ( 3, 16) is on the circle.
6 Figure 67. Parallelogram 68. Triangle 69. Rhombus/Kite 70. Circle 71. Trapezoid 72. Arc Length 73. Sector Formula CHAPTER The base and height in a figure are always what? Find the area of the shaded region The area of the shaded region is 276 cm 2. Find the value of x. 80. Find the area of the smaller sector. 81. Find the length of arc AB. 82. Find the area of the regular polygon. 83. Find the area of the shaded region. 84. Find the area of the shaded region. 85. Find the area of the shaded region.
7 86. PRISMS CHAPTER CYLINDERS 88. SPHERES 89. CONES 90. PYRAMIDS Find the Lateral Area, Surface Area, and Volume of the following solids cm
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