Honors Geometry Qtr 2 Practice from Chapters 5-8

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Block: Seat: Honors Geometry Qtr 2 Practice from Chapters 5-8 Short Answer 1. Use DEF, where J, K, and L are midpoints of the sides. If DE = 8x + 12 and KL = 10x 9, what is DE? 2. Use DEF, where J, K, and L are midpoints of the sides. If JL = 7x 6 and EF = 9x + 8, what is EK? 1

3. Use DEF, where J, K, and L are midpoints of the sides. If DF = 18x 6 and JK = 3x + 11, what is JK? 4. Find the value of x. 5. Find the value of x. 2

6. Find the value of x that makes P the incenter of the triangle. 7. Find the value of x that makes P the incenter of the triangle. 8. Find the coordinates of the centroid P of STU. S Ê Ë Á 2, 5 ˆ, T Ê Ë Á5, 2 ˆ, U Ê ËÁ 1, 6 ˆ 9. Find the coordinates of the centroid P of STU. S Ê Ë Á 1, 7 ˆ, T Ê Ë Á5, 6 ˆ, U Ê ËÁ 7, 4 ˆ 3

10. Point S is the centroid of PQR. Use the given information to find the value of x. QS = 3x + 5 and QT = 4x + 11 11. Point S is the centroid of PQR. Use the given information to find the value of x. VS = 3x 2 and VP = 7x + 4 12. Point S is the centroid of PQR. Use the given information to find the value of x. RS = 4x + 1 and SU = 3x 4 4

13. List the sides and angles in order from smallest to largest. 14. List the sides and angles in order from smallest to largest. 15. List the sides and the angles in order from smallest to largest. 16. List the sides and angles in order from smallest to largest. 5

17. Is it possible to build a triangle using the given side lengths? If so, order the angle measures of the triangle from least to greatest. AB = 73, BC = 3 10, AC = 5 7 18. Is it possible to build a triangle using the given side lengths? If so, order the angle measures of the triangle from least to greatest. JK = 33, KL = 4 5, JL = 9 3 19. Complete the statement with <, >, or =. m 1? m 2 20. Complete the statement with <, >, or =. PQ? SR 21. Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 6

22. Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 23. Given similar triangles, write the ratios of corresponding sides in a statement of proportionality. EFG QRS 24. Given similar triangles, write the ratios of corresponding sides in a statement of proportionality. CBS NQP 25. Find the perimeter of polygon B given that polygon A and polygon B are similar. The ratio of corresponding sides of polygon A to polygon B is 3:4. The perimeter of polygon A is 12 meters. 26. Find the perimeter of polygon B given that polygon A and polygon B are similar. The ratio of corresponding sides of polygon A to polygon B is 2.5:1. The perimeter of polygon A is 10 feet. 27. Describe the dilation that moves EFG onto ERS. 7

28. Describe the dilation that moves EFG onto ERS. 29. The lengths of the legs of right triangle FGH are 12 meters and 16 meters. The shortest side of JKL is 2.4 meters and JKL FGH. How long is the hypotenuse of JKL? 30. In the diagram, LMN PQR. Find the scale factor of PQR to LMN. 8

31. In the diagram, LMN PQR. Find the length of the altitude shown in PQR. 32. In the diagram, LMN PQR. Estimate the lengths of LM and PQ. Round your answers to the nearest tenth. 33. Determine whether the triangles are similar. If they are, write a similarity statement. 9

34. Determine whether the triangles are similar. If they are, write a similarity statement. 35. Determine whether the triangles are similar. If they are, write a similarity statement. 36. Determine whether the triangles are similar. If they are, write a similarity statement. 10

37. Find the value of x. 38. Find the value of x. 39. Find the value of x. 11

40. Find the value of x. 41. Draw a dilation of the polygon with the given vertices using the given scale factor k. AÊ ËÁ 12, 6 ˆ,B Ê Ë Á B, 3 ˆ,C Ê Ë Á 3,6 ˆ,D Ê ËÁ 12,6 ˆ ; 1 6 12

42. Draw a dilation of the polygon with the given vertices using the given scale factor k. AÊ Ë Á 0,0 ˆ,B Ê Ë Á0,2 ˆ,C Ê Ë Á2,2 ˆ,D Ê ËÁ 4,0 ˆ ; k = 2.25 43. You take 450 U.S. dollars to the bank to exchange for European euros. The exchange rate on that day is about 0.82 euros per U.S. dollar. How many European euros did you get for the 450 U.S. dollars? 44. Find the value of x. Write your answer in simplest radical form. 45. Find the value of x. Write your answer in simplest radical form. 13

46. Find the value of x. Write your answer in simplest radical form. 47. Find the value of x. Write your answer in simplest radical form. 48. Classify the triangle as acute, right, or obtuse. 5, 7, 9 49. Classify the triangle as acute, right, or obtuse. 3, 5, 34 50. Classify the triangle as acute, right, or obtuse. 3.1, 4.5, 5.2 51. Classify the triangle as acute, right, or obtuse. 9, 15, 10 3 14

52. Find the exact value of x. 53. Find the exact value of x. 54. Find the exact value of x. 55. Find the exact value of x. 15

56. Find the value of each variable. Write your answer in simplest radical form. 57. Find the value of each variable. Write your answer in simplest radical form. 58. Find the value of each variable. Write your answer in simplest radical form. 59. Find the value of each variable. Write your answer in simplest radical form. 16

60. Find the value of x. Round your answer to the nearest tenth. 61. Find the value of x. Round your answer to the nearest tenth. 62. Find the value of x. Round your answer to the nearest tenth. 63. Find the value of x. Round your answer to the nearest tenth. 17

64. Find the value of x. Round your answer to the nearest tenth. 65. Find the value of x. Round your answer to the nearest tenth. 66. Solve the right triangle. Round your answer to the nearest tenth. 67. Solve the right triangle. Round your answer to the nearest tenth. 18

68. A balloon rises to the ceiling of a gymnasium. You want to find the distance from the ground to the balloon. You use a cardboard square to line up the balloon and the ground. Your friend measures the vertical distance from the ground to your eye and the distance from you to the gym wall. Approximate the distance from the ground to the balloon. 69. Find the value of x. 70. Find the value of x. 19

71. Find the value of x. 72. Find the value of x. 73. Find the value of x in the parallelogram. 74. Find the value of x in the parallelogram. 75. Find the value of x in the parallelogram. 20

76. Find the value of x in the parallelogram. 77. Find the value of x in the parallelogram. 78. Find the value of x in the parallelogram. 79. Three of the ABCD are given. Find the coordinates of point D. AÊ Ë Á 3, 6 ˆ, B Ê Ë Á6, 7 ˆ, C Ê ËÁ 6, 3 ˆ, DÊ ËÁ x, yˆ 80. Three of the ABCD are given. Find the coordinates of point D. AÊ Ë Á 3, 4 ˆ, B Ê Ë Á 3, 2 ˆ, C Ê ËÁ 1, 4 ˆ, DÊ ËÁ x, yˆ 81. Three of the ABCD are given. Find the coordinates of point D. AÊ Ë Á 6, 0 ˆ, B Ê Ë Á0, 4 ˆ, C Ê ËÁ 4, 2 ˆ, DÊ ËÁ x, yˆ 82. Three of the ABCD are given. Find the coordinates of point D. AÊ Ë Á 1, 0 ˆ, B Ê Ë Á4, 1 ˆ, C Ê ËÁ 2, 4 ˆ, DÊ ËÁ x, yˆ 21

83. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. CM MX 84. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. ZX CM 85. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. Z M 86. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. ZM CX 87. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. CM ZX 88. For any rectangle CMXZ, decide whether the statement is always, sometimes, or never true. CMZ XZM 89. Find the value of x. 90. Find the value of x. 22

91. Find the value of x. 92. Find the value of x. 93. Give the most specific name for the quadrilateral. 94. Give the most specific name for the quadrilateral. 95. Give the most specific name for the quadrilateral. 23

96. Give the most specific name for the quadrilateral. 97. In the kite shown, m ADC = 105 and m DAB = 100. Find m DCB. 24

Honors Geometry Qtr 2 Practice from Chapters 5-8 Answer Section SHORT ANSWER 1. ANS: 32 2. ANS: 22 3. ANS: 18 4. ANS: x = 10 5. ANS: x = 48 6. ANS: x = 5 7. ANS: x = 7 8. ANS: Ê ËÁ 2, 1 ˆ 1

9. ANS: Ê ËÁ 1, 1 ˆ 10. ANS: x = 7 11. ANS: x = 5 12. ANS: x = 9 2 13. ANS: BC, AC, AB; A, B, C 14. ANS: FH, HG, FG; G, F, H 15. ANS: PR, QR, PQ; Q, P, R 16. ANS: TU, ST, SU; S, U, T 17. ANS: yes; C, A, B 2

18. ANS: no 19. ANS: < 20. ANS: = 21. ANS: x < 21 22. ANS: x < 9 2 23. ANS: EF QR = FG RS = GE SQ PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 24. ANS: CB NQ = BS QP = SC PN PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 25. ANS: 16 m PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 3

26. ANS: 4 ft PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 27. ANS: The figure shows a dilation with center E and scale factor 1 3. PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 28. ANS: The figure shows dilation with center E and scale factor 2. PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 29. ANS: 4 m PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 30. ANS: 8 5 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 31. ANS: 11 1 5 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 32. ANS: LM = 8.1,PQ = 13.0 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 33. ANS: similar; ABE CBD PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 4

34. ANS: not similar PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 35. ANS: similar; JKL JMN PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 36. ANS: similar; EHD GHF PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 37. ANS: x = 16 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 38. ANS: x = 7 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 39. ANS: x = 10.2 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 40. ANS: x = 5 PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 6 Test, Form C 5

41. ANS: PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.CO.2 TOP: Chapter 6 Test, Form C 42. ANS: PTS: 1 DIF: Level C NAT: NT.CCSS.MTH.10.9-12.G.CO.2 TOP: Chapter 6 Test, Form C 43. ANS: $369 PTS: 1 DIF: Level C TOP: Chapter 6 Test, Form C 44. ANS: 25 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.8.8.G.7 TOP: Chapter 7 Test, Form B 45. ANS: 55 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.8.8.G.7 TOP: Chapter 7 Test, Form B 6

46. ANS: 6 5 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.8.8.G.7 TOP: Chapter 7 Test, Form B 47. ANS: 2 29 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.8.8.G.7 TOP: Chapter 7 Test, Form B 48. ANS: obtuse PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 49. ANS: right PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 50. ANS: acute PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 51. ANS: acute PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 52. ANS: 15 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 7 Test, Form B 53. ANS: 1 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 7 Test, Form B 54. ANS: 12 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 7 Test, Form B 7

55. ANS: 2 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 7 Test, Form B 56. ANS: x = 6 3, y = 3 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 57. ANS: x = 19, y = 7 2 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 58. ANS: x = 2 6, y = 3 2 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 59. ANS: x = 7, y = 2 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 60. ANS: x 6.5 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 61. ANS: x 4.2 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 62. ANS: x 5.1 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 63. ANS: x 28.3 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 8

64. ANS: x 14.0 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 65. ANS: x 9.3 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 66. ANS: AC = 10, m A 53.1, m C 36.9 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 67. ANS: EG 16.5, EF 7.9, m G 28.6 PTS: 1 DIF: Level B TOP: Chapter 7 Test, Form B 68. ANS: 20 ft PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 7 Test, Form B 69. ANS: 97 70. ANS: 70 71. ANS: 150 72. ANS: 50 9

73. ANS: 29 74. ANS: 8 75. ANS: 6 76. ANS: 37 77. ANS: 3 78. ANS: 60 79. ANS: Ê ËÁ 3, 2 ˆ 80. ANS: Ê ËÁ 1, 2 ˆ 81. ANS: Ê ËÁ 2, 2 ˆ 10

82. ANS: Ê ËÁ 3, 3 ˆ 83. ANS: sometimes 84. ANS: always 85. ANS: always 86. ANS: always 87. ANS: never 88. ANS: always 89. ANS: 6 90. ANS: 51 11

91. ANS: 7 92. ANS: 2 93. ANS: kite 94. ANS: rectangle 95. ANS: rhombus 96. ANS: trapezoid 97. ANS: 50 PTS: 1 DIF: Level B NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 TOP: Chapter 8 Test, Form B 12

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