Name Date Class GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET For 1 2, use the graph. 6. State the converse of the statement. Then determine whether the converse is true. Explain. If two angles are vertical angles, then they are congruent. _ 1. Which segment is congruent to EF? 7. Use the graph. 2. What is the midpoint of GH? Use the following information for 3 4. In the figure, m KJL = 32. Write the vector that maps RST to R S T. _ Use the figure for 8 9. 3. What is the value of x? 4. What is m KJM? 5. Line segment PQ with endpoints P(4, 2) and Q( 2, 0) is rotated 90 clockwise around the origin. What are the coordinates of the midpoint of PQ? 8. How many lines of symmetry does the figure have? _ 9. What are the angles of rotation less than 360 for the figure? _ 191
Name Date Class Use the following information for 10 11. In the figures below, ABC LNM. 13. The measures of two complementary angles are represented by theexpressions (3x + 16) and (5x + 18). Find the value of x. _ 10. What is the value of x? 11. What is the value of y? 12. In the figure, m 2 = 75. 14. Write an equation for the line that passes through (1, 3) and is perpendicular to 1 y = x + 5. 2 _ 15. Write an equation for the line that passes through (3, 2) and is parallel to 2x + 3y = 3. _ 16. In the figure, the measure of 2 is 55. What is m 7? What is the measure of 4? _ 192
Name Date Class 17. Use the figures. 21. In the figure, PQ PS. Determine the value of x that ensures that the triangles are congruent. For 18-19, state the additional congruency statement or statements needed to prove ABC XYZ for the given theorem. Explain why PQR PSR. 22. In the figure, m BAC = 9x + 4 and m BAD = 3x + 8. 18. ASA Theorem 19. AAS Theorem 20. Look at the figure below. What value of x indicates that AD is the angle bisector of BAC? _ 23. Use the figure. What is the value of x? Are triangles DEF and FGH congruent? Explain why or why not. If the triangles are congruent, write a congruence statement. _ 24. The sum of the measures of the interior angles of a regular polygon is 900. How many sides does the polygon have? _ 193
Name Date Class 25. Triangle RST is an isosceles triangle with m R = 120. What is m S? Explain your reasoning. 30. In the figure, LP, MP, and NP are perpendicular bisectors. 26. The sides of a triangle measure 5 meters and 8 meters. What are the possible side lengths for the third side? Show your work. For 27-28use the figure. If LP = 5, LH = 12, HP = 13, and PM = 6, what is PJ? _ 31. ABCD is a quadrilateral with BE ED and BCD DAB. 27. If EG = 4, what is GC? 28. If AF = 15, what is AG? If EC = 16 cm, m ABC = 64, AE = 3x 5, and m DAB = (4y 12), for what values of x and y is ABCD a parallelogram? 29.In the figure, MN is the midsegment of JKL. If KM = 11 cm and KL = 24 cm, what is KN? 194
Name Date Class 32. State whether each quadrilateral has congruent diagonals. A parallelogram Yes No B rhombus Yes No C rectangle Yes No D isosceles trapezoid Yes No E kite Yes No 33. GIJL is a trapezoid with midsegment HK. 35. A parallelogram has vertices D( 4, 1), E(2, 5), F(4, 3), and G( 2, 3). Determine whether DEFG is a rhombus, rectangle, or neither. Explain your reasoning. The figure is symmetric about the x-axis. If IJ = 18 cm and GL = 42 cm, what is HK? 34. Triangle PQR is shown in the graph. 36. Find the perimeter of the figure. Round to the nearest tenth. _ 37. What is the area of the figure? _ Classify the triangle. Explain your reasoning. 195
Name Date Class Use the following information for 38-39. Triangle ABC has vertices A( 6, 2), B( 2, 2), and C(4, 8). Dilate ABC using a factor of 1 about the origin. Then dilate 2 its image using a scale factor of 5 about the origin. 38.Determine the coordinates of the final image. 43. If CD = 8, FG = 12, and GH = 24, what is the length of BC? _ Use the figure for 44-45. 39. Determine the scale factor you could use to dilate ABC about the origin that would result in the final image in one step. 40. CDE maps to LMN with the transformation 2 2 ( x, y) ( x + 3, y 2) x, y. 3 3 If CD = 9, what is LM? 44. Which triangles are similar? Write a similarity statement. _ 45.What is AB? _ 46.Use the figure to find the unknown distance. Use the following information for 41-42. Polygons BCDE and FGHI are similar. 41. Write a proportion that contains BE and CD. 42. List any angles that are congruent to DEB. What is the distance across the river? 196
Name Date Class 47. Rectangles ABCD and EFGH are similar. Rectangle ABCD has a length of 20 cm and a perimeter of 60 cm. Rectangle EFGH has a length of 32 cm. Find the area of rectangle EFGH. Use triangle XYZ for 52-53. Round to the nearest tenth. Use the following information for 53 55. In the figure, PS = 4 and SQ = 16. Find each length to the nearest tenth. 52. What is YX? _ 53. What is YZ? _ Use the triangle below for questions 54-55. Round to the nearest tenth. 48.What is the length of RS? 49.What is the length of RP? 50.What is the length of RQ? 51.Use the figure. 54. If m A = 50, m B = 100, and b = 15 cm, what is a? _ 55.If a = 12 cm, b = 18 cm, and c = 8 cm, what is m A? _ What is the length of FE? 197
Name Date Class 56. In the figure, m KJL = (12x + 8) and m KML = (10x + 16). Use the circle for 60-62. 60. Find the exact arc length of QR. What is the value of x? 57 In the circle, m WX = 50 and myz = 130. _ 61. Convert the central angle to radians. 62. What is the area of the sector formed by RPQ to the nearest tenth? _ What is m V? Use the circle for 58-59. In the circle, mad = 38 and mbc = 162. 63. Write an equation of a circle with center (3, 4) and radius 2. 64. Find the center and radius of the circle with the following equation. 2 2 x x y y 6 + + 4 3= 0 _ 58.What is m AED? 59.If DE = 3, EB = 16, and AE = 4, what is EC? 198
Name Date Class Use the information for 65-66. A prism has 6-inch square bases and a height of 10 inches. A cylinder has a diameter of 10 inches and a height of 6 inches. 65. Which solid has the greater volume? 66. Which solid has the greater surface area? 67. The oblique cylinder shown below has a volume of 36π cubic inches. What is the radius of the base of the cylinder to the nearest tenth of an inch? 68. A right cone has a slant length of 9 centimeters and a radius of 4 centimeters. What is the surface area of the cone? Round to the nearest tenth of a square centimeter. _ 70.A square pyramid and a cube have equal volumes. The side length of the base of each figure is 16 millimeters. How many times taller is the pyramid than the cube? _ 71. A cylinder has a radius of 8 inches and a height of 16 inches. The radius of a cone is half the length of the radius of the cylinder. If the cylinder and the cone have equal volumes, how many times greater is the height of the cone than the height of the cylinder? _ Use the following information for 80 81. A company sells several sizes of the same design of trash cans. The trash cans consist of a cylinder and a hemisphere. The smallest size trash can has the dimensions shown. 69. The triangular prism has a surface area of 510 square meters. Find the missing value for x. DIAGRAM IS AT TOP OF NEXT COLUMN 72.What is the volume of the trash can to the nearest tenth of a cubic inch? _ 199