Geometry B Semester REVIEW
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1 Geometr Semester REVIEW Name 1. What is the solution of the proportion? 2. The measures of the angles of a triangle are in the extended ratio 2 : 6 : 10. What is the measure of the smallest angle? 3. salsa recipe uses green pepper, onion, and tomato in the extended ratio 1 : 3 : 8. How man cups of onion are needed to make 2 cups of salsa?. The polgons are similar, but not necessaril drawn to scale. Find the value of x. 5. In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the diagram, the trees are 3.1 centimeters apart. How far apart should the actual trees be planted? 6. State whether the triangles are similar. If so, write a similarit statement and the postulate or theorem ou used. O 27 J 9 M 9 K 3 N 7. ampsites F and G are on opposite sides of a lake. surve crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. 70 m
2 8. Which theorem or postulate proves the two triangles are similar? (Not drawn to scale) > > 9. Michele wanted to measure the height of her school s flagpole. She placed a Not mirror drawn on to the scale. ground 35 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her ees were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. 35 ft. 10. What similarit statement can ou write relating the three triangles in the diagram? T U V W 11. What is the value of x, given that? P 6 x Q Find the length of the missing side. The triangle is not drawn to scale. 8 15
3 13. Wane used the diagram to compute the distance from Ferris, to Dunlap, to utte. How much shorter is the distance directl from Ferris to utte than the distance Wane found? Ferris 15 mi Dunlap 20 mi utte 1. In triangle, is a right angle and 5. Find. If our answer is not an integer, leave it in simplest radical form. 12 ft Not drawn to scale 15. Find the value of the variable(s). If our answer is not an integer, leave it in simplest radical form. 7 x 60 1 Not drawn to scale 16. Find the value of x and rounded to the nearest tenth. x The students in Mr. ollin s class used a surveor s measuring device to find the angle from their location to the top of a building. The 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. uilding 150 ft
4 18. Find the value of x. Round to the nearest tenth. 15 x Not drawn to scale 19.Write the ratios for sin X and cos X. X 5 12 Z 119 Y 20. Find the value of x. Round to the nearest degree. 20 x 11 Not drawn to scale 21. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. 10 w 11 x 22. What is the description of as it relates to the situation shown?
5 23. To approach the runwa, a pilot of a small plane must begin a 10 descent starting from a height of 1983 feet above the ground. To the nearest tenth of a mile, how man miles from the runwa is the airplane at the start of this approach? 1983 ft x Not drawn to scale 2. Use the Law of Sines to find side b of the triangle. 50 b Use the diagram. Find the translation rule that describes the translation D. E x D What translation rule can be used to describe the result of the composition of and? x
6 27. The vertices of a triangle are P(7, 5), Q(1, 7), and R( 3, 8). Name the vertices of. x 28. Describe the transformation shown in each image x x 2. D x x 2
7 29. The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. Find. R F G Q H P O I N J M L K 30. Use the figures below. Write a sequence of rigid motions that maps to. 8 T E D S R F P 8 8 x X Y The dashed-lined figure is a dilation image of with center of dilation P (not shown). Is an enlargement, or a reduction? What is the scale factor n of the dilation? 8 ' 8 8 x ' ' 8
8 8 ft 16 ft 32. The zoom feature on a camera lens allows ou dilate what appears on the displa. When ou change from 100% to 300%, the new image on our screen is an enlargement of the previous image with a scale factor of 3. If the new image is 6 millimeters wide, what was the width of the previous image? 33. blueprint for a house has a scale factor n = 5. wall in the blueprint is 9 in. What is the length of the actual wall? 3. Find the area. The figure is not drawn to scale. 9 cm 8 cm 17 cm 9 cm 19 cm 35. Find the area. The figure is not drawn to scale. 36. What is the area of the kite? 6 ft 6 ft
9 37. Find the area of the trapezoid. 5 cm 9 cm 5 2 cm 38. Given the regular polgon, find the measure Not drawn of to each scale numbered angle You are planning to use a ceramic tile design in our new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures centimeters, what will be the exact area of each hexagonal shape? cm 0. The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale. 32 d 28 d 1. The trapezoids are similar. The area of the smaller trapezoid is 709 m. Find the area of the larger trapezoid to the nearest whole number. 27 m 39 m Not drawn to scale
10 2. Find the measure of. The figure is not drawn to scale. E D O Find the circumference. Leave our answer in terms of. 18 in.. Find the area of the circle. Leave our answer in terms of. 2.2 m 5. Find the area of the figure to the nearest tenth. 150 o 15 in. 6. Find the probabilit that a point chosen at random from is on the segment. J 0 K L M N O P Q R S T Find the probabilit that a point chosen at random will lie in the shaded area.
11 8. Use Euler s Formula to find the missing number. Edges: 27 Faces: 17 Vertices:? 9. Describe the cross section. 50. 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. 51. Find the surface area of the clinder in terms of. 10 cm 17 cm Not drawn to scale 52. Use formulas to find the lateral area and surface area of the given prism. Round our answer to the nearest whole number m 26 m 19 m
12 53. Find the surface area of the cone to the nearest tenth. 13 cm 5. Find the surface area of the regular pramid shown to the nearest whole number. 55. Find the volume of the given prism. Round to the nearest tenth if necessar. 56. Find the volume of the given prism. Round to the nearest tenth if necessar.
13 57. Find the volume of the clinder in terms of. 58. Find the volume of the sphere shown. 1 cm 59. If the similarit ratio of two similar solids is : 10, what is the ratio of their corresponding areas? What is the ratio of their corresponding volumes? 60. is tangent to. If and, what is? The diagram is not to scale. O 61. ircle O and circle P are congruent. Given, what can ou conclude from the diagram? J K O H P N... and D. none of these L M
14 62. Find the value of x. If necessar, round our answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale O x 63. Find m in circle O. (The figure is not drawn to scale.) O 6. is tangent to circle O at. If, what is m Y? (The figure is not drawn to scale.) Y O 65. Find the value of x. If necessar, round our answer to the nearest tenth. The figures are not drawn to scale. = 18, = 8, and D = 9 x D 66. and. Find m. (The figure is not drawn to scale.) D E
15 67.Find the value of x. If necessar, round our answer to the nearest tenth. The figures are not drawn to scale. 5 7 x 2 68., and is tangent to the circle at R. Find m U. (The figure is not drawn to scale.) R S T U 69. low-wattage radio station can be heard onl within a certain distance from the station. On the graph below, the circular region represents that part of the cit where the station can be heard, and the center of the circle represents the location of the station. Write the equation that represents the boundar for the region where the station can be heard? 8 8 O 8 x Write the standard equation for the circle with center (10, 6) and radius = drug trial is testing the effectiveness of two drugs. If 50 patients are given Drug, 90 patients are given Drug, and 30 patients are given a placebo, what is the probabilit that a patient will NOT be given a placebo? 72. In a batch of 390 water purifiers, 10 were found to be defective. What is the probabilit that a water purifier chosen at random will be defective? Write the probabilit as a percent.
16 73. student rolls two non-standard number cubes in a probabilit experiment. Use the results in the frequenc table below to determine the experimental probabilit of rolling at least one three. Result 1, 1 1, 2 2, 2 1, 3 2, 3 3, 3 Frequenc The results of a surve of students favorite animal are organized in the frequenc table below. What is the relative frequenc of the preference for cats? nimal Frequenc Dog 9 at 6 ird 6 Mouse 10 Snake 75. Suppose Ruth nn has routes she can choose from to get from school to the librar, and 6 routes from the librar to her home. How man routes are there from Ruth nn s school to her home with a stop at the librar? 76. While organizing a film festival, ou must decide which of the 11 movies will be shown on the big screen. You onl have the budget to show 9 movies on this screen, and ou want to be able to tell moviegoers which order the films will be shown. In how man different was can ou show 9 of the 11 movies on the big screen? 77. In how man different orders can 12 basketball plaers be listed in a program? 78. local pizzeria offers 11 toppings for their pizzas and ou can choose an 5 of them for one fixed price. How man different tpes of pizzas can ou order with 5 toppings? 79. pet store has two tanks of tropical fish. The first tank contains blue fish and 9 ellow fish and the second tank contains 7 blue fish and 8 ellow fish. If Keisha randoml purchases a fish from each tank, what is the probabilit that both fish will be blue? 80. On St. Patrick s Da, ou took note of who was coming into our restaurant wearing green. The two-wa frequenc table shows the results of our surve. What is the probabilit that a randoml chosen customer will be a female wearing green? Round to the nearest thousandth. Wearing Green Yes No Totals Male Female Totals
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