Geometry Second Semester Final Exam Review

Name:Class:Date:ID: AGeometry Second Semester Final Exam Review1. Mr. Jones has taken a survey of college studentsand found that 1 out of 6 students are liberal artsmajors. If a college has 7000 students, what is thebest estimate of the number of students who areliberal arts majors?a. 1167b. 117c. 210d. 42,0002. Mr. Jones has taken a survey of college studentsand found that 90 out of 106 students are liberalarts majors. If a college has 7596 students, whatis the best estimate of the number of studentswho are liberal arts majors?a. 45b. 8946c. 64,494d. 6449ED EC3. Given that , find BC to the nearestBABCtenth. The figure is not drawn to scale.5. Two ladders are leaning against a wall at the sameangle as shown. How long is the shorter ladder?a. 8 ftb. 22 ftc. 18 ftd. 36 ft6. Shown below is an illustration of the .a. 40.5b. 0.2c. 38.3d. 21.34. The triangles below are similar. Find x.a.b.c.d.a. AA Similarity Postulateb. SAS Congruence Theoremc. SSS Similarity Theoremd. SAS Similarity Theorem7. The postulate or theorem that can be used toprove that the two triangles are similar is .a.b.c.d.3.193.524.9991SAS Similarity TheoremASA Congruence TheoremSSS Similarity TheoremAA Similarity Postulate

11. Solve:35x 31128. Given: PQ BC. Find the length of AQ.12.Solve the proportion57 .x 1x13.Solve the proportion37 .2x5a. 11b. 9c. 13d. 69. Find the value of x to one decimal place.14. A survey indicated that 4 out of 6 doctors usedbrand X aspirin. If 3600 doctors were surveyed,how many used brand X?a. 2.2b. 22.5c. 0.5d. 19.010. For the figure shown, which statement is nottrue?ED EC , find AB to the nearestBABCtenth. The figure is not drawn to scale.15. Given thata.b.c.d.w x yzwx yzwz xyw y xz2

16. Determine whether the figures are similar.17. In the diagram, ΔABC is similar to ΔEDC. Writethe statement of proportionality.21. Sadie wants to find the height of the tallestbuilding in her city. She stands 130 feet awayfrom the building. There is a tree 37 feet in frontof her, which she knows is 17 feet tall. How tall isthe building? (Round to the nearest foot.)18. Given that ΔABC ΔDEF, solve for x and y.22. State the postulate or theorem that can be usedto prove that the two triangles are similar.23. State the postulate or theorem that can be usedto prove that the two triangles are similar.19. A building casts a shadow 200 meters long. At thesame time, a pole 4 meters high casts a shadow20 meters long. What is the height of thebuilding?20. A building casts a shadow 168 meters long. At thesame time, a pole 5 meters high casts a shadow20 meters long. What is the height of thebuilding?24. Given: ΔBCD ΔEFG. Find the length of BC.3

25. Tell whether each pair of triangles is similar.Explain your reasoning.28. Given AE Ä BD. Solve for x.26. If p Ä q, solve for x.29. Find EF.27. Given: PQ BC. Find the length of AC.30. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.31. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.a.8.062b.17.748c.46.0984d.18.028

32. How long is a string reaching from the top ofa 12-ft pole to a point on the ground that is 6 ftfrom the bottom of the pole? Give an exactanswer and an approximation to 3 decimal places.33. A 25.5 foot ladder rests against the side of ahouse at a point 24.1 feet above the ground. Thefoot of the ladder is x feet from the house. Findthe value of x to one decimal place.a.b.c.d.1.97.08.310.134. Find a, b, and h.35. Find the length of the altitude drawn to thehypotenuse.38. Find the value of x and y.39. Find the value of x and y.36. Find the value of x.a.32b.36c.3540. Find the value of x.d. 3 3037. Find the value of the variable in the diagram.41. Find tan A for the right triangle below:5

42. Explain how a tangent ratio can be used to findthe height of the building in the figure below. Findthe height of the building when A 35 .43. A photographer shines a camera light at a particular painting forming an angle of 47 with the cameraplatform. If the light is 52 feet from the wall where the painting hangs, how high above the platform is thepainting?a. 0.93 ftb.44. Find sin P, cos P, tan P.55.76 ftc.1.07 ft45. Write the trigonometric ratio.A. sin AC . cos Ad.48.49 ft47. A slide 4.4 m long makes an angle of 33 withthe ground. How high is the top of the slide abovethe ground?B. tan Ba. 2.53 mb. 2.4 mc. 3.69 md. 2.86 m48. Liola drives 19 km up a hill that is at a grade ofo15 . What horizontal distance, to the nearesttenth of kilometer, has she covered?46. To find the height of a tower, a surveyorpositions a transit that is 2 meters tall at a spot40 meters from the base of the tower. Shemeasures the angle of elevation to the top of thetower to be 46 . What is the height of the tower,to the nearest meter?a.b.c.d.65.1 km4.9 km14.2 km18.4 km

49. Find the value of x, to the nearest whole number. (not drawn to scale)50. Find x, to the nearest hundredth.54. An airplane is flying at an elevation of 1500feet. What is the airplane's angle of elevationfrom the runway when it is 5000 feet from therunway? Explain.55. An antenna is atop the roof of a 100-footbuilding, 10 feet from the edge, as shown in thefigure below. From a point 50 feet from the baseof the building, the angle from ground level to thetop of the antenna is 66 . Find x, the height ofthe antenna, to the nearest foot.o51. Solve the right triangle: α 20 and a 20;Find β, b, and c.52. Find the missing angle and side measures ofΔABC, given that m A 20 , m C 90 , andCB 20.ç56. The translation vector is u 〈 7, 4〉. If theˆÊ image of A is A ′ Á 6 , 4 , find the coordinates Ë of point A.ç57. The translation vector is u 〈7, 3〉. The imageˆ Ê of point A is A ′ Á 5 , 7 . Find the coordinates Ë of A.a. m B 110 , c 58.5, b 55.4b. m B 70 , c 59, b 54.9c. m B 70 , c 58.5, b 54.9d. m B 110 , c 58.5, b 54.953. Two legs of a right triangle have lengths 15 and8. The measure of the smaller acute angle is.a.b.c.d. 32.2 17 61.9 28.1 58. The point A(–7, 3) is translated onto A ′ by theçvector u 〈5, 4〉. The coordinates of A ′ are.a. (–2, –1)b. (–12, 7)c. (2, –7)d. (5, –4)7

59. The points in a coordinate plane are reflected inthe y-axis. In general, every point (x, y) ismapped onto what point?61. Suppose the triangle in the figure below isreflected over the y-axis. Draw the line ofreflection and the image triangle.60. The points in a coordinate plane are reflected inthe line y x. In general, every point (x, y) ismapped onto what point?62. Name the transformation.ˆ Ê 64. Graph the figure with vertices Á 4, 4 , Ë ˆˆˆ ÊÊÊ , Á 1, 5 , and Á 1, 7 . Rotate theÁ 2, 2 Ë Ë Ë figure 180 about the origin.63. Name the transformation.65. Name the transformation. (Preimages areunshaded; images are shaded.)8

66. The hexagon shown below is equiangular. Howmany lines of symmetry does it have?71. Does the clock face below have any rotationalsymmetry? If so, list any angles of rotation, 180 or less, that can map it onto itself.a. 2b. 1c. 3d. 667. For the figure below, draw all the lines ofsymmetry. If there are none, write "none."72. Tell whether the figure has rotational symmetry.If so, give each angle and direction of rotationthat produces rotational symmetry.68. Which of the following letters (if drawn assimply as possible) has at least one line ofsymmetry?Q , S, T, Z73. Given RP 22, RA 6, and PQ is tangent to ñRat Q, find PQ.a. Sb. Tc. Qd. Z69. How many lines of symmetry does a regularhexagon have? Sketch the symmetry lines on thefigure below.74. Given ST is tangent to ñR at S, find RT.70. How many lines of symmetry does an isoscelesright triangle have? Draw a diagram to illustrate.9

78. Given circle O with radius 34 and OC 16. Findthe length of AB.75. Given: In ñO, mBAC 320 . Find m A.a.b.c.d.26 13 20 10 79. Given circle O with radius 25 and OC 7. Findthe length of AB.76. Given: In ñO, mBAC 298 . Find m B.80. Find the value of x to the nearest tenth.a. 37 b. 31 c. 15.5 d. 18.5 77. Find the value of x.a.b.c.d.10.014.811.317.110

81. Find m PSQ if m PSQ 3y 5 and m PRQ 2y 15.85. Find the measure of 1.86. Find the measure of 1.a.b.c.d.27.5 20 55 35 87. Find the value of x.82. Given ñQ and m B 62 , find mAC.a.b.c.d.62 124 236 248 a. 18b. 12c. 6d. 988. Find the value of x.83. Find the value of x if mAB 20 and mCD 62 .a. 41 b. 21 c. 43 d. 20.5 84. Find the measure of 1.a.b.c.d.112412189

89. Find the value of x.91. Find the area (not drawn to scale):a. 8b. 6c. 3d. none of these90. Find the value of x.92. The area of the parallelogram is .a.b.680 sq. units800 sq. unitsc.d.40 111 sq. units340 sq. units93. Find the area of the region shown by dividing itinto two trapezoids.a.b.c.d.158none of these3594. Find the area:12

95. Find the area of the quadrilateral.100. Each circle is tangent to the other two. If thediameter of the large circle is 12, the area of theshaded region is .a.b.c.d.96. Circle O has a radius of 7.39. If m AOB is 112 ,then find the length of AB to one decimal place.9 π sq. units36 π sq. units18 π sq. units24 π sq. units101. Find the area of the shaded region.97. Find the arc length of AB to two decimal places.2a. 123.15 cm2b. 38.48 cm2c. 153.94 cm2d. 30.79 cm102. Find the area of a regular heptagon with sidelength 10 cm.98. Find the area of the shaded region. (Assume thatthe ends of the figure are semicircles.)2a. 363.4 cm2b. 346.7 cm2c. 403.3 cm2d. 726.8 cm103. Find the surface area of the right prism below.99. Find the area of the shaded region. Use π 3.14.13

104. The right prism below has bases which areequilateral triangles of side length 4 cm. Its heightis 5 cm. Find its surface area.105. Find the surface area of the cylinder to thenearest square unit. Use π 3.14.107. Name the three dimesional solid which can beformed by this net.a. Triangular Prismb. Rectangular Prismc. Triangular Pyramidd. Rectangular Pyramid108. Sketch a net for the solid.a. 98 m2b. 307 m2c. 62 m2d. 614 m2106. The surface area, in square centimeters, of theright cylinder below is .109. The pyramid shown has a square base and a slantheight of 7 ft. Find its surface area.110. The surface area of the right cone shown is.a.b.c.d.ˆÊ 2 Á7 π 14π (12) 217πË 14π (12) 168π98π (14π )12 266πˆÊ 2 (12 ) 588πÁ7 π Ë 142a.b.c.44 π in.2112 π in.216 33 π in.d.36 π in.2

111. Find the volume of the right triangular prism.114. The pyramid shown has a rectangular base andfaces that are isosceles triangles. Find its volume.3a. 60 m3b. 288 m3c. 576 m3d. 36 m112. The volume of the right circular cylinder is about.115. Calculate the volume of the cone. Use π 3.14.3a. 265.5 m3b. 326.7 m3c. 1036.9 m3d. 1061.9 m113. A concrete block has a cylindrical hole 4 feet indiameter drilled through it to allow a pipe to passthrough. How many cubic feet of concrete areleft in the block? Use 3.14 as an approximationfor π and round your answer to the nearest tenth.a.b.c.d.3a. 301.44 m3b. 904.32 m3c. 37.68 m3d. 96 m116. Find the volume of the figure to the nearesttenth.90.0 cubic feet85.4 cubic feet140.6 cubic feet203.4 cubic feet15

117. What is the volume of a sphere with diameter 9.4feet?a.b.c.d.3434.9 ft3277.6 ft369.4 ft392.5 ft16

ID: AGeometry Second Semester Final Exam ReviewAnswer Section1.2.3.4.5.6.7.8.9.10.ADCBCDDBDB17317x 215x 142400 used brand X16.9The figures are not similar.EC DC DE AC BCBAx 5.25, y 5.3340 meters42 meters60 ftSAS Similarity TheoremAA Similarity Postulate40Yes; SAS Similarity Theorem122761439.592D11. 28.29.30.31.32.180 ft; 13.416 ft33. C34.35.36.37.a 18, b 366Da 82 , h 1221

ID: A38. x 53 , y 1039. x 11, y 1140. x 4741.243242. Using the tangent ratio tan A ˆleg opposite AÊoho , tan 35 . So h 150 Á tan 35 150 (0.7 ), or leg adjacent to A150Ë about 105 ft.43. B815844. sin P , cos P , tan P 171715abb45. A.B.C.cac46. 43 m47. B48. D49. 550. 10.07β 7051.ob 54.95c 58.4852. C53. Do54. About 72.5 . cosx 55.56.57.58.59.60.x 35 ft(13, –8)(–2, –4)A(–x, y)(y, x)1500 1 Ê 1500so x cos Á5000Ë 5000ˆ o 72.5 2