Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Architectural drawing wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Euclidean geometry wikipedia , lookup
Geometry Review of material to date for the Final Exam: Ch. 1-12 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name the ray in the figure. 4. If T is the midpoint of A B SU? S a. what are ST, TU, and T 9x U 6 x + 30 b. a. b. c. d. c. d. 2. What is the name of the ray that is opposite ST = 10, TU = 90, and SU = 180 ST = 110, TU = 110, and SU = 220 ST = 18, TU = 18, and SU = 36 ST = 90, TU = 90, and SU = 180 ? 5. bisects and Solve for x and find The diagram is not to scale. D C B A a. b. c. d. 3. What is the intersection of plane TUYX and plane VUYZ? a. b. c. d. x = 13, x = 13, x = 14, x = 14, 6. Noam walks home from school by walking 8 blocks north and then 6 blocks east. How much shorter would his walk be if there were a direct path from the school to his house? Assume that the blocks are square. a. 14 blocks b. 10 blocks c. 4 blocks d. The distance would be the same. a. b. c. d. 7. Find the circumference of the circle in terms of . 39 in. a. b. c. d. 156 in. 39 in. 1521 in. 78 in. 8. Find the area of a rectangle with base of 2 yd and a height of 5 ft. a. 10 yd b. 30 ft c. 10 ft d. 30 yd 12. Is the statement a good definition? If not, find a counterexample. A square is a figure with two pairs of parallel sides and four right angles. a. The statement is a good definition. b. No; a rhombus is a counterexample. c. No; a rectangle is a counterexample. d. No; a parallelogram is a counterexample. 13. a. b. c. d. bisects . Find 50 125 75 175 14. = 7x. Find 1 4 9. What conjecture can you make about the fourteenth term in the pattern A, B, A, C, A, B, A, C? a. The fourteenth term is B. b. The fourteenth term is C. c. The fourteenth term is A. d. There is not enough information. 10. Write this statement as a conditional in if-then form: All triangles have three sides. a. If a triangle has three sides, then all triangles have three sides. b. If a figure has three sides, then it is not a triangle. c. If a figure is a triangle, then all triangles have three sides. d. If a figure is a triangle, then it has three sides. 11. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional. Two lines that intersect at right angles are perpendicular. a. The statement is not reversible. b. Yes; if two lines intersect at right angles, then they are perpendicular. c. Yes; if two lines are perpendicular, then they intersect at right angles. d. Yes; two lines intersect at right angles if (and only if) they are perpendicular. = 2 3 Drawing not to scale a. b. c. d. 37 143 27 153 15. What is the relationship between 1 2 m 3 4 5 6 n 7 a. b. c. d. 8 corresponding angles same-side interior angles alternate interior angles alternate exterior angles and ? y 16. Find the value of x for which p is parallel to q, if .The diagram is not to scale. 10 8 6 (–8, 5) 3 4 5 4 2 1 2 6 –10 –8 –6 –4 –2 –2 2 4 6 8 10 x –4 p –6 q –8 a. b. c. d. (1, –8) –10 108 116 28 112 a. 17. Find the value of x for which l is parallel to m. The diagram is not to scale. 80° ( 3 x - 43 )º l 9 13 b. 13 9 c. 13 9 d. 9 13 m 20. What is the slope of the line shown? a. b. c. d. y 100 80 123 41 8 6 4 2 18. Find the values of x, y, and z. The diagram is not to scale. –8 –6 –4 –2 –2 35° (–8, –5) 11° 59° x° z° 2 4 (5, 0) 6 8 x –4 –6 –8 y° a. a. b. c. d. 19. What is the slope of the line shown? 13 5 b. 13 5 c. 5 13 d. 5 13 21. What is the equation in point-slope form for the line parallel to y = 3x + 2 that contains P(–7, –6)? y – 6 = 3(x + 7) x + 6 = –3(y + 7) y + 6 = –3(x + 7) y + 6 = 3(x + 7) a. b. c. d. a. b. c. d. none of these 22. Given and , find a. b. c. d. 24. State whether and Justify your answer. and 22 11 10 25 7 23. Name the angle included by the sides N 7 and M a. b. c. d. P 25. What is the missing reason in the two-column proof? Given: Prove: bisects and bisects N < are congruent. M O > P Statements Reasons 1. 2. 3. bisects 1. Given 2. Definition of angle bisector 3. Reflexive property 4. 5. 6. bisects 4. Given 5. Definition of angle bisector 6. ? a. ASA Postulate c. AAS Theorem yes, by either SSS or SAS yes, by SSS only yes, by SAS only No; there is not enough information to conclude that the triangles are congruent. b. SSS Postulate 26. What is the value of x? d. SAS Postulate 29. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 38° 21 150 ft 21 xº a. b. c. d. Drawing not to scale a. b. c. d. 71° 142° 152° 76° 75 ft 150 ft 35.5 ft 37.5 ft 30. Name a median for A 27. Find the value of x. The diagram is not to scale. | S E ) | | | D ) (3 x – 50)° R (7 x )° T U a. b. c. d. none of these 28. Which overlapping triangles are congruent by ASA? a. b. c. d. C F B a. b. c. d. 31. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides • bisectors of the angles • medians • lines containing the altitudes a. incenter circumcenter centroid orthocenter b. circumcenter incenter centroid orthocenter c. circumcenter incenter orthocenter centroid d. incenter circumcenter orthocenter centroid 32. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by and is 11 cm, the side included by and is 16 cm, and the side included by and is 14 cm. 35. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. x x 1 2 3 4 a. b. c. d. 33. Find the sum of the measures of the angles of the figure. a. b. c. d. 18° 54° 36° 72° 36. Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 5-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 9-gon, one at each vertex. a. greater than b. cannot tell c. equal to d. less than 37. ABCD is a parallelogram. If then The diagram is not to scale. A a. b. c. d. 900 1080 1620 1260 34. What is the measure of one angle in a regular 25gon? a. b. c. d. B 194.4 4140 165.6 82.8 D a. b. c. d. C 66 124 114 132 38. For the parallelogram, if find scale. and The diagram is not to 3 A 4 2 B 4x – 2 1 y + 14 9 17 173 163 4y – 7 x + 28 39. ABCD is a parallelogram. If then The diagram is not to scale. A B D a. b. c. d. C x = 10, y = 38 x = 10, y = 21 x = 10, y = 7 x = 7, y = 10 42. In the rhombus, C 1 | D What are The diagram is not to scale. | a. b. c. d. 125 65 75 115 3 | | a. b. c. d. 2 40. If find so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. A D a. b. c. d. B C a. b. c. d. 43. The isosceles trapezoid is part of an isosceles triangle with a 46° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale. 39 282 141 78 41. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. a. 67°; 134° b. 67°; 113° c. 46°; 134° d. 46°; 113° d. 95.5 45. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower? a. 1 : 725 b. 725 : 1 c. 12 : 725 d. 725 : 12 44. What is LM? A B L M D 46. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the rectangle? a. 32 feet b. 48 feet c. 64 feet d. 96 feet C a. 171 b. 85.5 c. 79 What is the solution of each proportion? 47. a. b. c. d. Are the polygons similar? If they are, write a similarity statement and give the scale factor. S V 10 12 T 15 32º W R 32º U 18 Not drawn to scale. 48. a. b. ; ; c. ; d. The triangles are not similar. A 21.6 B N 1.8 K 9 9 4.68 4.68 D M C 21.6 1.8 L Not drawn to scale. 49. a. b. 50. ; 9 : 1.8 ; 21.6 : 1.8 c. ; 9 : 4.68 d. The polygons are not similar. The polygons are similar, but not necessarily drawn to scale. Find the value of x. a. 118 b. 29.5 c. 21.7 d. 177 52. Are the triangles similar? How do you know? 30.4° a. x = 8 b. x= 84.6° a. b. c. d. c. x = 9 d. x = 10 K yes, by SAS yes, by SSS yes, by AA no B J A L C 6 3 59 x D 51. M Which theorem or postulate proves the two triangles are similar? 84.6° 66° c. 53. 14 d. 28 > 7 56. What is value of x, given that ? > O Not drawn to scale. a. b. c. d. SSS Theorem AA Postulate AS Postulate SAS Theorem x Q 18 54. Use the information in the diagram to determine the height of the tree to the nearest foot. a. b. c. d. P 9 N 20 M a. b. c. d. x = 10 x = 20 x = 13 x = 25.5 57. Four explorers are trying to find the distance across an oddly shaped lake. They position themselves as shown in the diagram. Alhombra uses her compass to instruct Chou and Duong to move along the line they form with Bizet until she sees that from her perspective the angle between Bizet and Chou is equal to the angle formed between Chou and Duong. They measure the distance between Bizet and Chou to be 35 m, between Chou and Duong to be 46 m, and between Alhombra and Duong to be 100 m. How long is the lake from east to west? Round your answer to the nearest tenth of a meter. 80 ft 264 ft 60 ft 72 ft 55. What is the value of x, given that ? A x B 11 E 5 D 7 C a. b. a. b. c. d. 76.1 m 77.4 m 131.4 m 132.4 m 58. A triangle has side lengths of 28 in, 4 in, and 31 in. b. right Classify it as acute, obtuse, or right. c. acute a. obtuse Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. b. 42 ft; 35 min 59. c. 14 ft; 1 min d. 28 ft; 0.4 min x y 62. Find the missing value to the nearest hundredth. 30° tan 20 Not drawn to scale a. b. c. d. a. x = ,y= b. x = 10, y = c. x = , y = 10 d. x = 30, y = = 86 44.67 89.67 89.33 51.67 63. Write the tangent ratios for and . Z 60. A sign is in the shape of a rhombus with a 60° angle and sides of 9 cm long. Find its area to the nearest tenth. a. 70.1 cm2 b. 3.9 cm2 c. 7.8 cm2 d. 35.1 cm2 61. A conveyor belt carries supplies from the first floor to the second floor, which is 24 feet higher. The belt makes a 60° angle with the ground. 34 3 X 5 Y Not drawn to scale a. b. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor? a. 34 ft; 21 min Find the value of x. Round to the nearest tenth. c. d. d. 8.1 64. 10 x Not drawn to scale a. 12.9 b. 8.5 c. 12.4 65. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. a. b. c. d. 2400 ft 72 ft 308 ft 33 ft Building 100 ft Find the value of x. Round to the nearest degree. 66. 21 x 15 Not drawn to scale a. 41 b. 36 c. 46 d. 44 c. 70 d. 85 Find the value of x to the nearest degree. 67. 19 11 x Not drawn to scale a. 30 b. 60 Find the value of x. Round the length to the nearest tenth. 68. b. 10.4 yd c. 9 yd d. 31.2 yd x 18 yd Not drawn to scale a. 15.6 yd 69. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44 . To the nearest foot, what is the height of the pole? a. 145 ft b. 149 ft c. 135 ft d. 139 ft Use compass directions to describe the direction of the vector. (Not drawn to scale.) 70. N W E S a. 47 north of west b. 47 south of west c. 47 north of east d. 47 south of east Use the diagram. y E8 4 C –8 A –4 4 –4 8 x D B –8 71. Find the translation rule that describes the translation B a. c. b. d. A. 72. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of the image reflected across the y-axis. a. c. b. d. The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles. F R G Q H P I O N J M L K 73. Find the image of after a rotation of 240° about point O. a. b. c. d. Find the area. The figure is not drawn to scale. 75. 74. Find the angle of rotation about O that maps P to G. a. 240° b. 120° c. 210° d. 270° c. 13 yd2 d. 15 yd2 36 in. 77. 40 in. 33 in. 9 cm 8 cm a. b. c. d. 1188 in.2 69 in.2 138 in.2 1440 in.2 13 cm 76. 9 cm 3 yd 10 yd a. b. c. d. 11 cm 144.5 cm2 127 cm2 172 cm2 50 cm2 a. 30 yd2 b. 6.5 yd2 Find the area of a parallelogram with the given vertices. 78. P(1, 3), Q(3, 3), R(7, 8), S(9, 8) 79. Find the area of the regular polygon. Round your a. 10 units2 answer to the nearest tenth. b. 5 units2 c. 20 units2 d. none of these 81. The triangles are similar. The area of the larger triangle is 1589 ft . Find the area of the smaller triangle to the nearest whole number. 40 ft 13.07 in. 35 ft 10 in. a. b. c. d. Not drawn to scale 2 176.6 in. 966.1 in.2 80.0 in.2 483.0 in.2 80. The area of a regular octagon is 35 cm . What is the area of a regular octagon with sides three times as long? a. 315 cm b. 225 cm c. 175 cm d. 105 cm a. b. c. d. 1217 ft 1225 ft 1600 ft 2075 ft 82. Find the similarity ratio and the ratio of perimeters for two regular octagons with areas of and a. 3 : 5; 3: 5 b. 9 : 25; 3 : 5 c. 3 : 5; 9 : 25 d. 9 : 25; 9 : 25 Find the area of the regular polygon. Give the answer to the nearest tenth. 83. hexagon with a side of 8 yd 86. Identify a semicircle that contains C. a. 332.6 yd b. 12 yd C c. 41.6 yd d. 166.3 yd A 84. pentagon with a radius of 8 m a. 304.3 m b. 152.2 m c. 30.4 m d. 154.2 m 85. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35 . To the nearest hundredth, find the search area. a. 2.08 mi b. 2.97 mi c. 1.04 mi d. 1.49 mi B 0 a. b. c. d. 87. Name the major arc and find its measure. A A E D C )50° 103° B 27° D 50° B 35° O C a. b. c. d. ; 50 ; 50 ; 310 a. b. c. d. 130 230 140 120 ; 310 88. Find the measure of . The figure is not drawn to scale. Find the area of the circle. Leave your answer in terms of . a. 89. b. c. d. 74.2 in.2 8.2 in.2 148.4 in.2 23.6 in.2 4.1 m 92. Find the area of the shaded region. Leave your answer in terms of and in simplest radical form. a. b. c. d. 4.2025 m2 8.405 m2 16.81 m2 11.2 m2 90. A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel? a. 195.1 cm2 b. 97.5 cm2 c. 27.5 cm2 d. 390.1 cm2 91. Find the area of the figure to the nearest tenth. a. b. c. d. none of these 93. Find the probability that a point chosen at random from is on the segment . A B C D E F G H I 0 a. 105° 9 2 4 6 8 J K 10 b. 96. The radius of the base of a cylinder is 39 in. and its height is 33 in.. Find the surface area of the cylinder in terms of . a. 5583 in. b. 5577 in. c. 5688 in. d. 5616 in. c. d. 94. Find the probability that a point chosen at random will lie in the shaded area. 97. Find the surface area of the cone in terms of . 17 cm 14 3 cm Not drawn to scale a. b. c. d. a. b. c. d. 0.32 0.62 0.94 0.02 95. A circular dartboard has a radius of 2 meters and a red circle in the center. Assume you hit the target at a random point. For what radius of the red center region does P(hitting red) = 0.6? a. 77 m b. 1.2 m c. 1.55 cm d. 1.32 m Find the volume of the cylinder in terms of 111 cm 57 cm 60 cm 55.5 cm 98. The lateral area of a cone is 558 cm . The radius is 31 cm. Find the slant height to the nearest tenth. a. 17.1 cm b. 16.4 cm c. 18 cm d. 11.6 cm . c. 54 in. d. 324 in. 99. h = 6 and r = 3 a. 27 in. b. 108 in. 100. 5 in. 14 in. 6 mm 11 mm 9 mm Not drawn to scale a. b. c. d. Not drawn to scale 140 in. 175 in. 350 in. 70 in. 101. Find the volume of the composite space figure to the nearest whole number. a. b. c. d. 416 mm 705 mm 1294 mm 944 mm 102. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in. and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid? a. 10 in. b. 21 in. c. 28 in. d. 42 in. Find the volume of the cone shown as a decimal rounded to the nearest tenth. 103. 17 yd 8 yd Not drawn to scale a. 2421.1 yd In the figure, b. 1709 yd and c. 142.4 yd are tangent to circle O and d. 1139.4 yd bisects . The figure is not drawn to scale. B D O C A P 104. For a. 40 105. = 50, find . b. 50 c. 65 d. 140 is tangent to circle A at B and to circle D at C (not drawn to scale). AB = 10, BC = 21, and DC = 8. Find AD to the nearest tenth. B C A D a. 22.5 b. 21.1 c. 23.3 106. Pentagon RSTUV is circumscribed about a circle. Solve for x for RS = 10, ST = 13, TU = 11, UV = 12, and VR = 12. The figure is not drawn to scale. R 107. x V S U T d. 27.7 a. b. c. d. 4 8 11 6 The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is not drawn to scale.) a. b. c. d. C A B 57 28.5 33 114 109. In the circle, . Find m BCP. (The figure is not drawn to scale.) O a. b. c. d. A 12.4 3.8 24.9 44.4 D B 108. Find the measure of drawn to scale.) Q BAC. (The figure is not C P A a. b. c. d. 49 98 196 82 O 57º C B 110. and . Find m A. (The figure is not drawn to scale.) D B A C E a. 32.5 b. 65 c. 95.5 111. A footbridge is in the shape of an arc of a circle. The bridge is 4.5 ft tall and 25 ft wide. What is the radius of the circle that contains the bridge? Round to the nearest tenth. a. 39.2 ft b. 71.7 ft c. 19.6 ft d. 34.7 ft 112. Find the diameter of the circle for BC = 13 and DC = 24. Round to the nearest tenth. (The diagram is not drawn to scale.) Describe the locus in space. 113. points 5 cm from a point C a. a sphere of radius 5 cm, centered at C b. a circle of radius 5 cm, centered at C c. an endless cylinder with radius 5 cm d. a hemisphere of radius 5 cm, centered at C 114. points 3 in. from plane K a. a circle of radius 3 cm, centered at K b. two planes parallel to plane K, each 3 in. from K c. two lines parallel to plane K, each 3 in. from K d. a sphere of radius 3 cm, centered at K d. 96.5 D C B O A a. b. c. d. 31.3 44.3 11.2 57.3