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Name _______________________________________ Date __________________ Class __________________ Math One Plus: End-Of-Year Practice Test Modules 16–25 For 45–46, use the graph. 49. 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? ________________________________________ 50. Use the graph. 45. Which segment is congruent to EF ? _______________________________________ 46. What is the midpoint of GH ? _______________________________________ Use the following information for 47–48. In the figure, mKJL 32. Which transformation maps RST to R ST ? A (x, y) (x 6, y 6) B (x, y) (x 6, y 6) C (x, y) (x 6, y 6) D (x, y) (x 6, y 6) Use the figure for 51–52. 47. What is the value of x? _______________________________________ 48. What is mKJM? _______________________________________ 51. How many lines of symmetry does the figure have? ________________________________________ 52. What are the angles of rotation less than 360 for the figure? ________________________________________ Name _______________________________________ Date __________________ Class __________________ End-of-Year Test Modules 16–25 Use the following information for 53–54. In the figures below, ABC LNM . 57. In the figure, m2 75. 53. What is the value of x? _______________________________________ What is m7? 54. What is the value of y? ________________________________________ _______________________________________ Use the graph for 55–56. 58. The measures of two complementary angles are represented by the expressions (3x 16) and (5x 18) Find the value of x. ________________________________________ 59. Write an equation for the line that passes through (1, 3) and is perpendicular to 1 y x 5. 2 ________________________________________ 55. What transformations can you use to show that quadrilaterals DEFG and D'E'F'G' are congruent? _______________________________________ _______________________________________ 60. Write an equation for the line that passes through (3, 2) and is parallel to 2x 3y 3. ________________________________________ 61. In the figure, the measure of 2 is 55. 56. Express the transformations as a single mapping rule in the form of (x, y) (?, ?). _______________________________________ What is the measure of 4? ________________________________________ Name _______________________________________ Date __________________ Class __________________ End-of-Year Test Modules 16–25 62. Use the figures. Determine the value of x that ensures that the triangles are congruent. _______________________________________ For 63–64, state the additional congruency statement or statements needed to prove ABC XYZ for the given theorem. 63. ASA Theorem _______________________________________ 64. AAS Theorem _______________________________________ 65. Look at the figure below. 66. In the figure, PQ PS. Explain why PQR PSR. ________________________________________ ________________________________________ 67. Use the figure. Answer True or False for each statement. A Angle MKL is an exterior angle of triangle JKM. True False B Angle KML is an exterior angle of triangle JKM. True False C Angles MKL and KLM are complementary. True False D x = 35 True Are triangles DEF and FGH congruent? Explain why or why not. If the triangles are congruent, write a congruence statement. _______________________________________ _______________________________________ False 68. The sum of the measures of the interior angles of a regular polygon is 900. How many sides does the polygon have? ________________________________________ Name _______________________________________ Date __________________ Class __________________ End-of-Year Test Modules 16–25 69. Triangle RST is an isosceles triangle with mR 120. What is mS? Explain your reasoning. 74. In the figure, LP, MP, and NP are perpendicular bisectors. _______________________________________ _______________________________________ 70. The lengths of two sides of a triangle are 5 meters and 8 meters. If x represents the length of the third side in meters, which inequality gives all possible lengths for the third side? If LP 5, LH 12, HP 13, and PM 6, what is PJ? A 3 x 13 ________________________________________ B 3 x 13 75. In the figure, point W is the incenter of triangle XYZ. C x 3 or x 13 D x 3 or x 13 For 71–72, use the figure. If RW 5 and WY 14, what is WT? ________________________________________ 71. If EG 4, what is GC? 76. ABCD is a quadrilateral with BE ED and BCD DAB. _______________________________________ 72. If AF 15, what is AG? _______________________________________ 73. In the figure, MN is the midsegment of JKL. If EC 16 cm, mABC 64, AE 3x 5, and mDAB (4y 12), for which values of x and y is ABCD a parallelogram? A x 7, y 19 B x 32, y 7 C x 7, y 32 If KM 11 cm and KL 24 cm, what is KN? D x 8, y 19 _______________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 4 Name _______________________________________ Date __________________ Class __________________ End-of-Year Test Modules 16–25 77. State whether each quadrilateral has congruent diagonals. 80. 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. A parallelogram Yes No B rhombus Yes No C rectangle Yes No D isosceles trapezoid Yes No ________________________________________ E kite Yes No ________________________________________ 78. GIJL is a trapezoid with midsegment HK. 81. KLMN is an isosceles trapezoid. If IJ 18 cm and GL 42 cm, what is HK? What is the missing x-coordinate of N? _______________________________________ ________________________________________ 79. Triangle PQR is shown in the graph. Use the following information for 82–83. The figure is symmetric about the x-axis. Use the coordinates of the vertices to determine whether each statement is True or False. A Triangle PQR is a right triangle. True 82. Find the perimeter of the figure. Round to the nearest tenth. False B Triangle PQR is scalene. True ________________________________________ False C Triangle PQR is isosceles. True 83. What is the area of the figure? False ________________________________________ D Triangle PQR is an acute triangle. True False Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 5 Name _______________________________________ Date __________________ Class __________________ Answer Key End-of-Year Test Modules 16–25 angles are the acute base angles of the triangle. The sum of the base angles is 180 120 60, so each base angle is equal to 30. 45. AB 46. (3.5, 1.5) 47. x 7 70. A 48. 70 71. 8 49. (1, 1) 72. 10 50. D 73. 12 cm 51. 5 74. 13 52. 72, 144, 216, 288 75. 5 53. x 9 54. y 8 55. a reflection over the y-axis, then a translation 1 unit left and 6 units down 56. (x, y) (x 1, y 6) 57. 105 58. x 7 59. y 2x 1 2 60. y x 4 3 61. 35 62. x 9 63. AC XZ 64. AB XY or BC YZ 65. Yes; the figure shows that DF GF and EF HF . DFE and GFH are vertical angles, so DFE GFH. Therefore, DEF GHF by SAS. 66. It is given that PQR and PSR are right triangles and PQ PS. PR PR by the Reflexive Property, so PQR PSR by HL Theorem. 67. A False B True C False D True 68. 7 sides 69. mS 30; the base angles of an isosceles triangle are congruent. Since R is an obtuse angle, the unknown Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 6 Name _______________________________________ Date __________________ Class __________________ 76. C 77. A No B No C Yes D Yes E No 78. 30 cm 79. A False B False C True D True 80. rectangle; using the Distance Formula, DE FG 6 2, EF DG 2 2, so the figure has opposite sides that are congruent. The slope of DE slope of GF 1 and slope of EF slope of DG 1, so the figure has two pairs of parallel sides, and consecutive sides are perpendicular. Therefore, the figure is a rectangle. 81. 2a b 82. 19.3 units 83. 24 square units Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 7