Name: ate: 1. raw all lines of symmetry for these shapes. 4. windmill has eight equally-spaced blades that rotate in the clockwise direction. 2. Use the figure below to answer the question that follows. How many lines of symmetry does the figure have? 3. Which of the following figures appears to have both line symmetry and rotational symmetry?. B... Note: The figure is not drawn to scale. How many degrees must blade P rotate to reach the location of blade U?. 45 B. 135. 225. 300 page 1
5. fan has 5 congruent blades that are spaced equally as shown below. 7. The coordinates of the endpoints of ST and its image S T are given below. S(2, 4) S ( 2, 4) T( 1, 1) T (1, 1) Which of the following single transformations maps ST to S T? What is the measure of the angle of rotation if blade M moves clockwise to the position of blade P?. 36 B. 45. 60. 72 6. The coordinates of the endpoints of ST and its image S T are given below. S(2, 4) S ( 2, 4) T( 1, 1) T (1, 1) Which of the following single transformations maps ST to S T?. translation 4 units to the left B. rotation 180 clockwise about the origin. reflection over the x-axis. reflection over the y-axis. translation 4 units to the left B. rotation 180 clockwise about the origin. reflection over the x-axis. reflection over the y-axis 8. The coordinates of the endpoints of ST and its image S T are given below. S(2, 4) S ( 2, 4) T( 1, 1) T (1, 1) Which of the following single transformations maps ST to S T?. translation 4 units to the left B. rotation 180 clockwise about the origin. reflection over the x-axis. reflection over the y-axis 9. The point G(2, 7) is transformed according to the rule (x, y ) = (x+2, y 3). The image G of the transformation is then reflected over the line y = x, resulting in point G. What are the coordinates of G?. (4, 10) B. (4, 10). ( 10, 4). ( 4, 10) page 2
10. playground is in the shape of hexagon BEF. Which of the following is the best approximation of the amount of fencing needed to enclose the perimeter of this playground? 12. Triangle JKL is shown on the grid below. What is the length of KL? Round the answer to the nearest tenth of a unit.. 75 yards B. 80 yards. 85 yards. 90 yards. 3.2 units B. 4.0 units. 11.4 units. 11.7 units 11. Look at the triangle below. 13. triangle has vertices at (1, 3), (2, 3), and ( 1, 1). What is the approximate perimeter of the triangle?. 10 B. 14. 15. 16 What is the perimeter of the triangle? Round the answer to the nearest tenth of a unit.. 9.3 units B. 12.0 units. 20.6 units. 86.0 units page 3
14. Jill drew a circle in the coordinate plane. She then drew a diameter of the circle from ( 3, 2) to (5, 2) as shown below. 17. Points M and H are shown on the coordinate grid below. What is the length of the diameter of the circle that Jill drew? Round the answer to the nearest unit.. 4 units B. 5 units. 9 units. 12 units 15. What is the distance between the points (4, 2) and ( 5, 3)?. = 106 B. = 28. = 26. = 2 16. The point (12, 5) is units away from the origin.. 13 units B. 25 units. 144 units. 169 units Point M is the midpoint of GH. What are the coordinates of point G?. (0, 1) B. (2, 1). (4, 2). (12, 7) 18. If M( 2, 5) is the midpoint of B and the coordinates of are (4, 7), what are the coordinates of B?. (1, 6) B. (2, 12). (8, 6). ( 8, 3) 19. What is the midpoint of the line segment joining points (3, 5) and ( 6, 1)?. ( 4.5, 3) B. ( 3, 6). ( 1.5, 3). (1.5, 2) 20. In parallelogram B, the coordinates of are (4, 3) and the coordinates of the midpoint of diagonal are (2, 5). What are the coordinates of? page 4
21. Points P(2, 9) and Q(8, 7) are on a coordinate grid. What are the coordinates of the midpoint of PQ? 24. Ms. hen drew a diagram for a new patio in her backyard.. (3, 1) B. (5, 8). (6, 2). (10, 16) 22. circle has a center at (2, 3). One end point of a diameter is at (4, 2). What are the coordinates of the other endpoint of that diameter?. (6, 1) B. ( 2, 4) The measure of 1 is 3 times as large as the measure of 2. What is the measure of 2? 23.. (1, 5). (0, 4) SU intersects TV at point R. What is the value of x, in degrees?. 45 B. 67.5. 120. 135 25. Use the polygon below to answer the following question. What is the total number of degrees of the interior angles of this polygon?. 64 B. 360. 900. 1,080 page 5
26. Line l is parallel to line m. Line t is a transversal with angle measures as indicated below. 28. Lines l and m are parallel to one another and cut by transversals s and t. Note: The figure is not drawn to scale. What is the value of x?. 16 B. 20. 25. 32 27. In the drawing, what is the measure of angle y? What is the value of x?. 40 B. 80. 120. 140 29. In the figure shown below, RS is parallel to TU, and PT intersects RS at Q.. 40 B. 60 What is the measure of RPQ?. 80. 100 page 6
30. In the diagram below, lines h and j are parallel. Line k and line m intersect lines h and j. 32. Given the diagram below, what information is needed to prove that the lines are parallel? 31. Based on the angle measures in the diagram, what is m 1?. 50 B. 60. 120. 130. m 1 = m 3 B. m 1 = m 6. m 1 = m 7. m 1 = m 8 33. In the diagram below, 1 = 4. Find the measure of angle a, given that l m, m EFG = 30 and FH = FI.. 30 B. 60. 90. 120 Which of the following conclusions does not have to be true?. 3 and 4 are supplementary angles. B. Line l is parallel to line m.. 1 = 3. 2 = 3 page 7
34. Given: angle What is the first step in constructing the angle bisector of angle? 36. If B EF, which of the following completes this proportion? B E =?. raw ray. B. raw a line segment connecting points B and.. From points B and, draw equal arcs that intersect at.. EF B. F. B. E 37. Triangle PQR is similar to triangle EF as shown.. From point, draw an arc that intersects the sides of the angle at points B and. 35. ladder is placed against a fence that is 6 feet tall. The ladder extends 2 feet above the fence and 3 feet behind the fence. Which describes the relationship between the corresponding sides of the two triangles?.. PQ E = 4 6 PQ EF = 4 9 B.. PQ E = 6 4 PR E = 6 6 Note: The figure is not drawn to scale. Which proportion can be used to find the distance (x) between the bottom of the ladder and the bottom of the fence?. x 6 = 3 8 B. x 6 = 2 3. x 6 = 3 2. x 6 = 8 3 page 8
38. Two similar trapezoids are shown. 40. Jim is making a similar, large rectangle from a small rectangle as shown below. Which proportion must be true? What is the height of the large rectangle?. MN IJ = NK JG B. MN IJ = MN KL 41. Triangle EF is similar to triangle B.. MN NK = JG IJ. MN IJ = IJ HI 39. figure is shown below. What is the measure, in degrees, of F? Which of the following is similar to this figure? (The figures are not drawn to scale.). B... page 9
42. In the diagram below, quadrilateral FGHJ = quadrilateral RSTV. 43. In the diagram below, triangle B is similar to triangle XYZ. Which angle corresponds to Z?. B B.. X. Y 44. Quadrilateral FGHI is similar to quadrilateral PQRS. Based on the measurements in the diagram, what is m F? Which of the following statements is true?. 33 B. 90. 112. 125. I = Q B. G = S. P = G. H = R page 10
45. B and MNOP are similar parallelograms. 47. Quadrilateral PQRS is shown below. What is the perimeter of MNOP? 46.. 43.2 B. 44. 54. 56 If quadrilateral WXYZ is congruent to quadrilateral PQRS, what is the measure of W?. 45 B. 70. 112. 133 In the figure above, polygons BE and RSTUV are congruent. Which side must have the same length as side B? 48. Trapezoid QRST is congruent to trapezoid WXYZ. Which side corresponds to TQ?. XY B. YZ. ZW. WX. B. E. ST. TU 49. What is the slope of the line that is perpendicular to the line whose equation is 3x 2y = 8? 3 2 2 3. 2 B. 3. 3. 2 50. Which equation represents the line parallel to the y-axis and 4 units to the left of the y-axis?. x = 4 B. x = 4. y = 4. y = 4 page 11
51. Which is an equation of the line that passes through the point (2, 5) and is parallel to the x-axis?. x = 2 B. y = 2. x = 5. y = 5 52. Which pair of points will determine a line parallel to the y-axis?. (2, 3) and ( 1, 3) B. (2, 2) and ( 3, 3). (3, 2) and (3, 1). (2, 2) and ( 2, 2) 56. What is an equation of the line that passes through the point ( 2, 5) and is perpendicular to the line whose equation is y = 1 2 x + 5?. y = 2x + 1 B. y = 2x + 1. y = 2x + 9. y = 2x 9 57. Find an equation of the line passing through the point (5, 4) and parallel to the line whose equation is 2x + y = 3. 58. What is an equation of the line that passes through the point ( 2, 3) and is parallel to the line whose equation is y = 3 2 x 4? 53. Which equation represents a line that is perpendicular to the line whose equation is 2y = 3x + 7?. y = x + 7 B. 2y = 3x 3. y = 2 3 x 3. y = 3 2 x 3 54. The equation of a line is y = 2 3 x + 5. What is an equation of the line that is perpendicular to the given line and that passes through the point (4, 2)?. y = 2 3 x B. y = 2 3 x + 5 3. y = 3 2 x. y = 3 2 x + 6 59. The lines represented by the equations y + 2 1 x = 4 and 3x + 6y = 12 are. the same line B. parallel. perpendicular. neither parallel nor perpendicular. y = 2 3 x 2 3 B. y = 3 2 x 4. y = 3 2 x + 7. y = 3 2 x + 8 55. Find an equation of the line passing through the point (6, 5) and perpendicular to the line whose equation is 2y + 3x = 6. 60. Write an equation of the line that passes through the point (1, 6) and is parallel to the line whose equation is y = 3x 5. 61. Which is an equation of the line that passes through the point ( 2, 4) and is parallel to the line y = 3?. x = 2 B. y = 2. x = 4. y = 4 page 12
62. In the accompanying diagram, B and intersect at E. If m E = 2x + 40 and m EB = x + 20, find x. 66. In the accompanying diagram, parallel lines B and are cut by transversal GH at E and F, respectively. If m GEB = (2x 30) and m EF = (x + 15), find the value of x. 63. The accompanying diagram shows intersecting lines l and m. Solve for the value of x. 67. In the accompanying diagram, transversal EF intersects parallel lines B and at G and H, respectively. If m EGB = 2x + 40 and m FH = 3x 10, what is the value of x? 64. B and intersect at E. If m E = 5x 20 and m BE = x + 50, find, in degrees, m EB. 65. In the accompanying diagram, B is parallel to, and B and are cut by transversal EF at points G and H, respectively. If m EG = (2x + 30) and m EH = (x + 80), find x. 68. s shown in the diagram below, lines m and n are cut by transversal p. If m 1 = 4x + 14 and m 2 = 8x + 10, lines m and n are parallel when x equals. 1 B. 6. 13. 17 page 13
69. Which diagram shows a correct mathematical construction using only a compass and a straightedge to bisect an angle? 71. The diagram below shows the construction of line m, parallel to line l, through point P.. B... 70. straightedge and compass were used to create the construction below. rc EF was drawn from point B, and arcs with equal radii were drawn from E and F. Which theorem was used to justify this construction?. If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. B. If two lines are cut by a transversal and the interior angles on the same side are supplementary, the lines are parallel.. If two lines are perpendicular to the same line, they are parallel.. If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel. Which statement is false?. m B = m B B. 1 2 (m B) = m B. 2(m B) = m B. 2(m B) = m B page 14
72. Janet graphed a triangle on the coordinate grid shown. Janet rotated the triangle 90 clockwise about the origin to create figure B. What are the coordinates of the vertices of the figure B after the rotation?. ( 4, 4) B ( 4, 2) ( 1, 2). ( 4, 4) B ( 2, 4) ( 2, 1) B. (4, 4) B (2, 4) (2, 1). (4, 4) B (4, 2) (1, 2) page 15
Problem-ttic format version 4.4.279 c 2011 2016 Educide Software Licensed for use by nna Koltunova Terms of Use at www.problem-attic.com 12/12/2016 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. One B 20. (0, 7) 21. 22. B 23. 30 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
Teacher s Key Page 2 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 4 inches 50 B B 55. y 5 = 2 3 (x 6) 62. 40 63. 8 64. 112.5 65. 50 66. 45 67. 50 68. 69. 70. 71. 72. 56. B 57. y 4 = 2(x 5) 58. 59. B 60. y = 3x + 3 61.