NAME DATE PER. GEOMETRY PRE-AP SPRING FINAL EXAM REVIEW LAW OF SINES & COSINES

Transcription

1 NME TE PER. GEOMETRY PRE-P SPRING INL EXM REVIEW LW O SINES & OSINES 1.Solve the triangle if = 15, = 113, side b = 49. m = Round answers to the nearest whole number. a = b = Law of = 2. Would you use Law of Sines or Law of osines to find the length of? ind the length. Round your answer to the nearest foot. 15 ft ft ft QURILTERLS omplete each statement about parallelogram MRK & explain your answer. Why? 3. MKR 4. S Why? K R 5. RK and are supplementary. Why? M S

2 or each parallelogram, find the values of x, y, and z. 6. x = y = z = x y 118 z 7. x = y y = z 20 z = x 42 Use rhombus RSTV and the given information to find each value. If m RST = 67, find the m RSW. S 8. m RSW = T W 9. m STV = ind m SVT if m STV = 135 S R T V W 10. x = If m SWT = (2x + 8), find the value of x. S R T V W 11. x = R What is the value of x if m WRV = (5x + 15) and m WRS = (7x 19)? S T V R W V

3 Use rhombus and the given information to find each value. If m = 28, find m ind the value of x if m = (16x + 26). 14. If m = 34, find m. 15. ind the value of x if m = (4x + 6). 16. What is the value of x if m = (4x + 6) and m = (12x 18)? WXYZ is an isosceles trapezoid with bases WZ and XY and median MN. Use the given information to solve each problem. ind MN if WZ = 11 and XY = MN = X Y M N 18. XY = If MN = 10 and WZ = 14, find XY. W Z

4 19. x = If MN = 10x + 2, WZ = 21, and XY = 8x +19, find the value of x. X Y M N W Z is an isosceles trapezoid. etermine if each statement is TRUE or LSE (circle one) and explain your reasoning. 20. = Explain: TRUE or LSE 21. TRUE or LSE 22. and bisect each other. Explain: Explain: E TRUE or LSE Quadrilateral EGH is a rectangle. ind the value of x. m HEG = (12x + 1) and 23. x = m GE = (6x 1) H G J E 24. x = H = 5x 4 and EG = 6x 10 H G J E 25. x = J = 8x + 4 and EG = 24x 8 H G J E

5 PERIMETER & RE O POLYGONS ind the EXT area of each regular polygon. Write your final, EXT answer, with appropriate units, in the blank provided. ind the area of the equilateral triangle 26. = with the indicated apothem length: 3 m 27. = ind the area of the regular quadrilateral with the indicated radius: 6ξ2 in 28. = ind the area of the regular polygon with the given side length: 12 ft IRLE SIS Write the term that best describes the following definitions. 29. segment with both endpoints on the circle. 30. chord that goes through the center of a circle. 31. line or ray that intersects a circle at two points. 32. line or ray that intersects a circle at exactly one point. ind the EXT answer for each of the following and write it in the space provided. Leave your answers in simplest form In a given circle, the radius is 48 cm. ind the measure of the circle s diameter. In a given circle, the area is 36. ind the measure of the circles radius.

6 In a given circle, the diameter is 8 cm. ind the circumference of the circle. ind the area of circle P. ind the area of the circle: 8 15 P 38. ind the EXT area of the shaded region. 8 in XZ is a tangent to circle at Y. Y is a radius. ind the measure of YZ. X Y Z 40. ZY is tangent to circle X. YXZ = 60, YZ = 6ξ3. ind the length of XZ. Y Z X 41. ML and MN are tangent to circle O. LM = 6x + 2 and NM = 38. ind the value of x. O L M N

7 42. ind the perimeter of the quadrilateral ind the value of x x 44. ind the value of x. 12 x ind the value of x. 8 in. 13 PRISMS & PYRMIS raw the indicated views for the isometric drawing below. Isometric rawing: 46. Top View: 6 in. x ront 47. Left View: 48. ront View:

8 raw a net that would produce the indicated three-dimensional figure. 49. Triangular Prism: 50. Hexagonal Prism: ind the indicated measure for each of the prism described below. 51. V = V = 6 ind the volume of a cube with a base edge of 3 cm. 53. T = ind the Total rea of the right triangular prism V = The volume of a rectangular prism is 64 cubic feet. If one dimension were reduced to one-sixteenth it original length, a second dimension were doubled, and a third dimension remained unchanged, what would be its new volume? raw a net that would form the indicated three-dimensional object. 55. Square Pyramid: 56. Pentagonal Pyramid:

9 ind the indicated measure for each of the following pyramids. Leave answers EXT and in simplest form. ind the Lateral rea of the square pyramid. 57. L = 10 yd 58. V = 12 yd 12 yd ind the Volume of the square pyramid from #65. ind the correct answer for each of the following. Write your final answer, with corresponding units, in the blank provided. The Volume of a rectangular pyramid is 192 cubic 59. V = units. If its dimensions are reduced to one-fourth their original length. What is the Volume of the smaller pyramid? 60. actor = If the dimensions of a pyramid were increased to threehalves their original length, by what factor would you multiply the original area to obtain the area of the larger pyramid? YLINERS, ONES, & SPHERES ind the correct answer for each of the following. Write your final, EXT answer, with its corresponding units, in the blank provided. ind the Volume of the cylinder: cm 8 cm

10 62. The Lateral rea of a right circular cylinder is 60 square meters. The height is 12 m. ind the diameter of the base. 63. ind the Lateral rea of the right circular cone: 12 cm 5 cm 64. ind the Volume of the right circular cone: 25 m 7 m 65. The Volume of a right circular cone is 72 cubic centimeters, and its height is 2 cm. ind the length of the radius. 66. ind the Total rea of the sphere: 12 cm 67. ind the Volume of the sphere: 24 cm 68. The Total rea of a sphere is 144 square centimeters. ind its diameter.

11 69. The Volume of a cylinder is 120 m 3. If it s dimensions are reduced to one-half their original length, what would its new Volume be? RS, IRLES, & NGLES Write your final answer in the blank provided. Leave answers as EXT. In the diagram the measure of =? O 71. Given that XZ is a diameter, find YZ. X (4x +21) P ind the m VPY. If = 13 and = 5, then find. V W Y Z (3x + 40) (5x 10) P Z Y (3x) (6x 15) (6x 15) 74. ind the value of x x

12 ind. If r = 6 cm, find the EXT length of. 5 E O 135 O 77. If r = 6 cm, find the EXT area of sector O. 135 O 78. ind the EXT area of the shaded region ind the value of x. (2x + 7) (3x + 3) ind the measure of

13 Use for problems and are points of tangency. m = 50, m = 85, m = 36, and me =79. is a diameter. ind m ind me. 2 E 4 H 3 G J K ind m ind m ind m ind m 4. ind m TRNSORMTIONS. Map the image and give the new coordinates Reflect the image below 88. (, ) across the y-axis and write the coordinates of I (, ) the vertices of the new polygon. I N (, ) N (, ) L (, ) L

14 89. lines of symmetry raw the line(s) of symmetry for the object, then write how many total lines of symmetry it has in the blank at left. 90. S (, ) T (, ) U (, ) Translate the polygon according to the ordered pair translation, then state the coordinates of the new polygon. (x + 7, y 8) S Y T U (, ) Y (, ) 91. H (, ) (, ) Rotate the figure below 180, then state the new coordinates of its vertices. R (, ) (, ) H R 92. N (, ) (, ) ilate the figure below using E as your center and a scale factor of 3. E N