Honors Geometry Final Study Guide 2014 1. Find the sum of the measures of the angles of the figure. 2. What is the sum of the angle measures of a 37-gon? 3. Complete this statement: A polygon with all sides the same length is said to be. A. regular B. equilateral C. equiangular D. convex 4. Find the missing values of the variables. The diagram is not to scale. 113 116 x y 72 5. Find the value of x. The diagram is not to scale. (2x + 10)º 148º (2x)º 112º 6. The sum of the measures of two exterior angles of a triangle is 250. What is the measure of the third exterior angle? 7. Find the values of the variables in the parallelogram. The diagram is not to scale. 22 108 z y x 8. For the parallelogram, if and find The diagram is not to scale. 3 4 2 1 9. WXYZ is a parallelogram. Name an angle congruent to X Y N W Z [page 1]
10. What is the most precise name for quadrilateral ABCD with vertices A( 5, 4), B( 5, 1), C(0, 1), and D(0, 4)? 11. In the rhombus, Find the value of each variable. The diagram is not to scale. 3 2 1 12. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 25º 1 3 2 13. In rectangle KLMN, KM = and LN = 43. Find the value of x. K L N M 14. are base angles of isosceles trapezoid JKLM. If and 15. What is the value of x? A B L M D C 16. A quadrilateral has vertices What special quadrilateral is formed by connecting the midpoints of the sides? 17. All of the angles of a quadrilateral are congruent. Can the quadrilateral be a parallelogram? Explain. 18. A model is made of a car. The car is 7 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? 19. Red and grey bricks were used to build a decorative wall. The was. There were 140 bricks used in all. How many red bricks were used? [page 2]
20. The measure of two complementary angles are in the ratio 1 : 9. What are the degree measures of the two angles? 21. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 120 feet, what is the length of the rectangle? 22-24 What is the solution of each proportion? 22. 23. 24. 25. The two rectangles are similar. Which is the correct proportion for corresponding sides? 4 m 12 m 8 m 24 m A. B. C. D. 26. Are the following two polygons similar, if so what is the scale factor, and by what property are they similar? V S 10 W 18 12 32º U T 15 32º R Not drawn to scale. 27. Are the triangles similar? How do you know (similarity property)? 30.4 84.6 84.6 66 [page 3]
) 28. Are the two triangles similar? How do you know? J H 47 M 47 º K G 29. Write a similarity statement the relates all three triangles in order of their angles. U V T 30. Determine the geometry mean of 6 and 7 31. Determine the values of a and b. W ) 8 10 6 a b 32. What is the value of x? x x 2 > x + 5 x + 1 33. Find the length of the missing side. > 5 34. Find the length of the missing side 4 5 cm 9 cm Not drawn to scale [page 4]
35. The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure to the nearest tenth. 36. A triangle has sides of lengths 27, 79, and 84. Is it a right triangle? Explain. 37. A triangle has side lengths of 14 cm, 48 cm, and 50 cm. Classify it as acute, obtuse, or right. 38. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 24 45 Not drawn to scale 39. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form. 45 13 x Not drawn to scale 40. The area of a square garden is 50 m 2. How long is the diagonal? 41. Find the value of the variables; leave your answer in simplest radical form. y 20 30 x Not drawn to scale 42. Find the missing value to the nearest hundredth. tan = 87 43. Find the missing value to the nearest hundredth. cos = 4 21 [page 5]
44. Find the missing value to the nearest hundredth. sin = 1 12 45. Write the all ratios for and. Z 3 73 X 8 Y Not drawn to scale 46. Find the value of x. Round your answer to the nearest tenth x 14 Not drawn to scale 47. Viola drives 110 meters up a hill that makes an angle of 9 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? 48. Find the value of x. Round your answer to the nearest tenth. x 12 yd Not drawn to scale 49. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? 50. Find the area of the shape below: 50 in. 37 in. 27 in. [page 6]
51. Find the area of the shape below: 8 cm 16 cm 52. The area of a parallelogram is 200 cm 2 and the height is 25 cm. Find the corresponding base. 53. Find the area of the parallelogram formed by: P( 2, 1), Q(8, 1), R(1, 5), S(11, 5) 54. Find the area of the trapezoid. 19 in. 12.6 in. 14.5 in. 29.2 in. Not drawn to scale 55. Determine the area of the shape: 11 ft 19 ft 45 Not drawn to scale 56. Find the area of the rhombus. 8 m 8 m 8 m 8 m 57. The area of a regular hexagon is 60 in. 2 Find the length of a side. Round your answer to the nearest tenth. 58. Find the area of a regular hexagon with side length of 4 m. Round your answer to the nearest tenth. 59. The area of a regular octagon is 35 cm. What is the area of a regular octagon with sides eight times as long? 60. Two trapezoids have areas of 432 cm and 48 cm. Find their ratio of similarity. [page 7]
61. Determine the area of a pentagon with a side of 9 m 62. Determine the area of a square with a radius of 14 m 63. What are the minor arcs of? J H O K L 64. Name the major arc and find its measure. A D C )50 B 65. The circumference of a circle is 46 cm. Find the diameter, the radius, and the length of an arc of 130. 66. Find the area of the shaded portion of the figure. Dimensions are in feet. Leave your answer in terms of. The figure is not drawn to scale. 67. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. 68. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim? Show your work. [page 8]
69. Use Euler s Formula to find the missing number. Vertices: 11 Edges: 24 Faces:? 70. Pierre built the model shown in the diagram below for a social studies project. He wants to be able to show the inside of his model, so he sliced the figure as shown. Describe the cross section he created. 71. Determine the lateral area and the total surface area of the prism: 5 m 16 m 7 m Not drawn to scale 72. Determine the surface area of the cylinder in terms of pi. 10 cm 13 cm Not drawn to scale 73. The radius of the base of a cylinder is 37 mm and its height is 53 mm. Find the surface area of the cylinder in terms of. 74. Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in. 75. Find the surface area of a conical grain storage tank that has a height of 32 meters and a diameter of 16 meters. Round the answer to the nearest square meter. [page 9]
76. Find the slant height of the cone to the nearest whole number. 77. Determine the volume of the cylinder in terms of pi. h = 6 in. and r = 3 in. 78. Find the height of the cylinder. 79. What is the maximum volume of a pyramid that can fit inside a cube with a side length of 18 cm? 80. Determine the surface area of a sphere with radius of 20 m 81. Find the surface area of a sphere with a circumference of 101 in. Round to the nearest tenth. 82. Find the similarity ratio of a cube with volume 216 ft to a cube with volume 1728 ft. Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 83. 10 P Q x O [page 10]
84. is tangent to. If and, what is? The diagram is not to scale. B A C O 85. Use the diagram from #84 to solve: A satellite (B) is 3,600 miles from the horizon of Earth. Earth s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth s surface. 86. and are all tangent to circle O (not drawn to scale), and. JA = 6, AL = 10, and CK = 11. Find the perimeter of. J A B O L 87. Find the value of x. C K 23 5 O x 88. Find the value of x. D C O x A B [page 11]
89. Find the measure of BAC in circle O. (The figure is not drawn to scale.) A O 70º B C 90., and is tangent to the circle at R. Find m U. (The figure is not drawn to scale.) R S T U 91. is tangent to the circle at A and is tangent to the circle at C. Find m D for m B = 58. (The figure is not drawn to scale.) A B D C 92. Find the value of x. 7 10 x 22 93. Write the standard equation for the circle with center ( 10, 3), r = 2 [page 12]
94. These two noncongruent circles intersect at exactly one point. Their common tangent is 24 cm, and the distance between their centers is 25 cm. C 24 cm D r A B a. What is the sum of the two radii? b. Express the radius of circle B in terms of r (the radius of circle A). c. Find the radius of circle B. Show your work. 95. In a batch of 960 calculators, 9 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary. 96. Lynn and Dawn tossed a coin 40 times and got heads 25 times. What is the experimental probability of tossing heads using Lynn and Dawn s results? 97. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 4 or greater than 7 in a single spin? 98. You roll a standard number cube. Find P(number is not 2). 99. A student rolls two non-standard number cubes, each with the numbers 1 through 3 on it. Use the results in the frequency table below to determine the experimental probability of rolling two numbers with a sum of 4. Order does not matter. Result 1, 1 1, 2 2, 2 1, 3 2, 3 3, 3 Frequency 8 7 9 5 8 5 A. 14 C. 1 3 B. 1 D. 5 1 14 42 100. A yogurt shop offers 3 different flavors of frozen yogurt and 8 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping? 101. In how many different orders can you line up 5 cards on a table? 102. Evaluate. 103. Evaluate. 104. Suppose Q and R are independent events, and P(Q) = 0.12, P(R) = 0.24. Find P(Q and R). 105. Suppose S and T are mutually exclusive events, P(S) = 47%, and P(T) = 36%. Find P(S or T). 106. A jar contains 4 blue cubes, 3 blue spheres, 6 green cubes, and 6 green spheres. If you select an object at random, what is the probability that the object is green or a cube? [page 13]
Honor Geometry Final Answer Section 1. ANS: 900 REF: 6-1 The Polygon Angle-Sum Theorems 2. ANS: 6300 REF: 6-1 The Polygon Angle-Sum Theorems 3. ANS: B REF: 6-1 The Polygon Angle-Sum Theorems 4. ANS: x = 111, y = 64 REF: 6-1 The Polygon Angle-Sum Theorems 5. ANS: 45 REF: 6-1 The Polygon Angle-Sum Theorems 6. ANS: 110 REF: 6-1 The Polygon Angle-Sum Theorems 7. ANS: REF: 6-2 Properties of Parallelograms 8. ANS: 163 REF: 6-2 Properties of Parallelograms 9. ANS: C REF: 6-2 Properties of Parallelograms 10. ANS: rectangle REF: 6-4 Properties of Rhombuses, Rectangles, and Squares 11. ANS: x = 30, y = 60, z = 45 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares 12. ANS: REF: 6-4 Properties of Rhombuses, Rectangles, and Squares 13. ANS: 6.5 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares [page 14]
14. ANS: 154 REF: 6-6 Trapezoids and Kites 15. ANS: 28 REF: 6-6 Trapezoids and Kites 16. ANS: rhombus REF: 6-7 Polygons in the Coordinate Plane 17. ANS: Yes; the sum of the angle measures of a quadrilateral is 360. If all angles are congruent, each angle would have a measure of 90, so the figure would be a parallelogram (a rectangle, in fact). REF: 6-5 Conditions for Rhombuses, Rectangles, and Squares 18. ANS: 14 : 1 REF: 7-1 Ratios and Proportions 19. ANS: 100 REF: 7-1 Ratios and Proportions 20. ANS: 9 and 81 REF: 7-1 Ratios and Proportions 21. ANS: 45 feet REF: 7-1 Ratios and Proportions 22. ANS: 9 REF: 7-1 Ratios and Proportions 23. ANS: 3 REF: 7-1 Ratios and Proportions 24. ANS: REF: 7-1 Ratios and Proportions 25. ANS: B REF: 7-2 Similar Polygons 26. ANS: [page 15]
; REF: 7-2 Similar Polygons 27. ANS: no REF: 7-3 Proving Triangles Similar 28. ANS: yes, by AA REF: 7-3 Proving Triangles Similar 29. ANS: REF: 7-4 Similarity in Right Triangles 30. ANS: 42 REF: 7-4 Similarity in Right Triangles 31. ANS: REF: 7-4 Similarity in Right Triangles 32. ANS: 5 REF: 7-5 Proportions in Triangles 33. ANS: 3 REF: 8-1 The Pythagorean Theorem and Its Converse 34. ANS: 106 cm REF: 8-1 The Pythagorean Theorem and Its Converse 35. ANS: 17.6 cm REF: 8-1 The Pythagorean Theorem and Its Converse 36. ANS: no; REF: 8-1 The Pythagorean Theorem and Its Converse 37. ANS: right [page 16]
REF: 8-1 The Pythagorean Theorem and Its Converse 38. ANS: 12 2 REF: 8-2 Special Right Triangles 39. ANS: REF: 8-2 Special Right Triangles 40. ANS: 10 m REF: 8-2 Special Right Triangles 41. ANS: x =, y = 40 REF: 8-2 Special Right Triangles 42. ANS: 89.34 REF: 8-3 Trigonometry 43. ANS: 79.02 REF: 8-3 Trigonometry 44. ANS: 4.78 REF: 8-3 Trigonometry 45. ANS: REF: 8-3 Trigonometry 46. ANS: 15.6 REF: 8-3 Trigonometry 47. ANS: 108.6 m REF: 8-3 Trigonometry 48. ANS: 3.2 yd REF: 8-4 Angles of Elevation and Depression 49. ANS: [page 17]
39 REF: 8-4 Angles of Elevation and Depression 50. ANS: 1350 in. 2 REF: 10-1 Areas of Parallelograms and Triangles 51. ANS: 64 cm 2 REF: 10-1 Areas of Parallelograms and Triangles 52. ANS: 8 cm REF: 10-1 Areas of Parallelograms and Triangles 53. ANS: 60 units 2 REF: 10-1 Areas of Parallelograms and Triangles 54. ANS: 303.66 in. 2 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites 55. ANS: 120 ft 2 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites 56. ANS: 128 m 2 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites 57. ANS: 4.8 in. REF: 10-3 Areas of Regular Polygons 58. ANS: 41.6 m 2 REF: 10-3 Areas of Regular Polygons 59. ANS: 2240 cm REF: 10-4 Perimeters and Areas of Similar Figures 60. ANS: 3 : 1 REF: 10-4 Perimeters and Areas of Similar Figures 61. ANS: 139.4 m [page 18]
REF: 10-5 Trigonometry and Area 62. ANS: 392 m REF: 10-5 Trigonometry and Area 63. ANS: REF: 10-6 Circles and Arcs 64. ANS: ; 310 REF: 10-6 Circles and Arcs 65. ANS: 46 cm; 23 cm; 16.6 cm REF: 10-6 Circles and Arcs 66. ANS: REF: 10-7 Areas of Circles and Sectors 67. ANS: REF: 10-7 Areas of Circles and Sectors 68. ANS: [4] Answers may vary. Sample: If a basketball has a circumference of 30, then its diameter is. If the ball goes in exactly in the center of the rim, then there is a total of (18 9.549) inches or 8.551 inches on both sides of the ball. Therefore, there is half of this distance, or about 4.2 inches, between the ball and the rim. [3] correct methods used, but with a computational error [2] error in method [1] correct answer with no work shown REF: 10-6 Circles and Arcs 69. ANS: 15 REF: 11-1 Space Figures and Cross Sections 70. ANS: pentagon REF: 11-1 Space Figures and Cross Sections 71. ANS: [page 19]
230 m ; 454 m REF: 11-2 Surface Areas of Prisms and Cylinders 72. ANS: 180 cm REF: 11-2 Surface Areas of Prisms and Cylinders 73. ANS: 6660 mm REF: 11-2 Surface Areas of Prisms and Cylinders 74. ANS: 210 in. REF: 11-3 Surface Areas of Pyramids and Cones 75. ANS: 1030 m REF: 11-3 Surface Areas of Pyramids and Cones 76. ANS: 21 m REF: 11-3 Surface Areas of Pyramids and Cones 77. ANS: 54 in. REF: 11-4 Volumes of Prisms and Cylinders 78. ANS: 2.4 in. REF: 11-4 Volumes of Prisms and Cylinders 79. ANS: 1944 cm REF: 11-5 Volumes of Pyramids and Cones 80. ANS: 1,600 m REF: 11-6 Surface Areas and Volumes of Spheres 81. ANS: 3247.1 in REF: 11-6 Surface Areas and Volumes of Spheres 82. ANS: 1 : 2 REF: 11-7 Areas and Volumes of Similar Solids 83. ANS: [page 20]
80 REF: 12-1 Tangent Lines 84. ANS: 45 REF: 12-1 Tangent Lines 85. ANS: 1,381 miles REF: 12-1 Tangent Lines 86. ANS: 54 REF: 12-1 Tangent Lines 87. ANS: 12.5 REF: 12-2 Chords and Arcs 88. ANS: 71 REF: 12-2 Chords and Arcs 89. ANS: 35 REF: 12-3 Inscribed Angles 90. ANS: 9.5 REF: 12-4 Angle Measures and Segment Lengths 91. ANS: 64 REF: 12-4 Angle Measures and Segment Lengths 92. ANS: 15.4 REF: 12-4 Angle Measures and Segment Lengths 93. ANS: (x + 10) + (y 3) = 4 REF: 12-5 Circles in the Coordinate Plane 94. ANS: [4] a. 25 cm b. 25 r c. Let r + x represent the radius of circle B. x + 24 = 25 ; x = 7; r + 7 = 25 r; r = 9 r + x = 9 + 7 = 16; 16 cm [page 21]
[3] one computational error [2] incomplete work in part c OR correct answers with no work shown [1] only two parts correct REF: 12-1 Tangent Lines 95. ANS: 0.9% REF: 13-1 Experimental and Theoretical Probability 96. ANS: 5 8 REF: 13-1 Experimental and Theoretical Probability 97. ANS: 3 5 REF: 13-1 Experimental and Theoretical Probability 98. ANS: 5 6 REF: 13-1 Experimental and Theoretical Probability 99. ANS: C REF: 13-2 Probability Distributions and Frequency Tables 100. ANS: 24 REF: 13-3 Permutations and Combinations 101. ANS: 120 REF: 13-1 Experimental and Theoretical Probability 102. ANS: 15,120 REF: 13-3 Permutations and Combinations 103. ANS: 70 REF: 13-3 Permutations and Combinations 104. ANS: 0.0288 REF: 13-4 Compound Probability 105. ANS: 83% REF: 13-4 Compound Probability [page 22]
106. ANS: 16 19 REF: 13-4 Compound Probability [page 23]