Honors Midterm Review

Transcription

1 Name: Date: 1. Draw all lines of symmetry for these shapes. 4. A 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? A. B. Note: The figure is not drawn to scale. How many degrees must blade P rotate to reach the location of blade U? 5. A fan has 5 congruent blades that are spaced equally as shown below. C. D. What is the measure of the angle of rotation if blade M moves clockwise to the position of blade P? page 1

2 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? 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? A. translation 4 units to the left B. rotation 180 clockwise about the origin C. reflection over the x-axis D. reflection over the y-axis 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? A. translation 4 units to the left B. rotation 180 clockwise about the origin C. reflection over the x-axis D. 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? A. translation 4 units to the left B. rotation 180 clockwise about the origin C. reflection over the x-axis D. reflection over the y-axis page 2

3 10. A playground is in the shape of hexagon ABCDEF. 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. A. 75 yards B. 80 yards C. 85 yards D. 90 yards 11. Look at the triangle below. 13. A triangle has vertices at (1, 3), (2, 3), and ( 1, 1). What is the approximate perimeter of the triangle? 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. What is the perimeter of the triangle? Round the answer to the nearest tenth of a unit. What is the length of the diameter of the circle that Jill drew? Round the answer to the nearest unit. 15. What is the distance between the points (4, 2) and ( 5, 3)? page 3

4 16. The point (12, 5) is units away from the origin. 23. SU intersects TV at point R. What is the value of x, in degrees? 17. Points M and H are shown on the coordinate grid below. Point M is the midpoint of GH. What are the coordinates of point G? 18. If M( 2, 5) is the midpoint of AB and the coordinates of A are (4, 7), what are the coordinates of B? 24. Ms. Chen drew a diagram for a new patio in her backyard. 19. What is the midpoint of the line segment joining points (3, 5) and ( 6, 1)? 20. In parallelogram ABCD, the coordinates of A are (4, 3) and the coordinates of the midpoint of diagonal AC are (2, 5). What are the coordinates of C? 21. Points P(2, 9) and Q(8, 7) are on a coordinate grid. What are the coordinates of the midpoint of PQ? 22. A 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? The measure of 1 is 3 times as large as the measure of 2. What is the measure of 2? 25. Use the polygon below to answer the following question. What is the total number of degrees of the interior angles of this polygon? page 4

5 26. Line l is parallel to line m. Line t is a transversal with angle measures as indicated below. 29. In the figure shown below, RS is parallel to TU, and PT intersects RS at Q. Note: The figure is not drawn to scale. What is the value of x? 27. In the drawing, what is the measure of angle y? What is the measure of RPQ? 30. In the diagram below, lines h and j are parallel. Line k and line m intersect lines h and j. Based on the angle measures in the diagram, what is m 1? 28. Lines l and m are parallel to one another and cut by transversals s and t. 31. Find the measure of angle a, given that l m, m EFG = 30 and FH = FI. What is the value of x? page 5

6 32. Given the diagram below, what information is needed to prove that the lines are parallel? 34. Given: angle A What is the first step in constructing the angle bisector of angle A? 33. In the diagram below, 1 = A 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. 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? Which of the following conclusions does not have to be true? A. 3 and 4 are supplementary angles. B. Line l is parallel to line m. C. 1 = 3 A. C. x 6 = 3 8 x 6 = 3 2 B. D. x 6 = 2 3 x 6 = If ABC EDF, which of the following completes this proportion? AB ED = AC? D. 2 = 3 page 6

7 37. Triangle PQR is similar to triangle DEF as shown. 39. A figure is shown below. Which describes the relationship between the corresponding sides of the two triangles? Which of the following is similar to this figure? (The figures are not drawn to scale.) A. PQ DE = 4 6 B. PQ DE = 6 4 A. C. PQ EF = 4 9 D. PR DE = 6 6 B. 38. Two similar trapezoids are shown. C. Which proportion must be true? A. C. MN IJ = NK JG MN NK = JG IJ B. D. MN IJ MN IJ = MN KL = IJ HI D. 40. Jim is making a similar, large rectangle from a small rectangle as shown below. What is the height of the large rectangle? page 7

8 41. Triangle DEF is similar to triangle ABC. 43. In the diagram below, triangle ABC is similar to triangle XYZ. What is the measure, in degrees, of F? 42. In the diagram below, quadrilateral FGHJ = quadrilateral RSTV. Which angle corresponds to Z? A. B B. C C. X D. Y 44. Quadrilateral FGHI is similar to quadrilateral PQRS. Which of the following statements is true? A. I = Q B. G = S C. P = G D. H = R 45. ABCD and MNOP are similar parallelograms. Based on the measurements in the diagram, what is m F? What is the perimeter of MNOP? page 8

9 Which equation represents the line parallel to the y-axis and 4 units to the left of the y-axis? A. x = 4 B. x = 4 In the figure above, polygons ABCDE and RSTUV are congruent. Which side must have the same length as side BC? 47. Quadrilateral PQRS is shown below. C. y = 4 D. y = Which is an equation of the line that passes through the point (2, 5) and is parallel to the x-axis? A. x = 2 B. y = 2 C. x = 5 D. y = Which pair of points will determine a line parallel to the y-axis? A. (2, 3) and ( 1, 3) B. (2, 2) and ( 3, 3) If quadrilateral WXYZ is congruent to quadrilateral PQRS, what is the measure of W? 48. Trapezoid QRST is congruent to trapezoid WXYZ. Which side corresponds to TQ? C. (3, 2) and (3, 1) D. (2, 2) and ( 2, 2) 53. Which equation represents a line that is perpendicular to the line whose equation is 2y = 3x + 7? A. XY B. YZ C. ZW D. WX 49. What is the slope of the line that is perpendicular to the line whose equation is 3x 2y = 8? 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)? 55. Find an equation of the line passing through the point (6, 5) and perpendicular to the line whose equation is 2y + 3x = 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? page 9

10 57. Find an equation of the line passing through the point (5, 4) and parallel to the line whose equation is 2x + y = AB and CD intersect at E. If m AEC = 5x 20 and m BED = x + 50, find, in degrees, m CEB. 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? 59. The lines represented by the equations y x = 4 and 3x + 6y = 12 are 65. In the accompanying diagram, AB is parallel to CD, and AB and CD are cut by transversal EF at points G and H, respectively. If m EGA = (2x + 30) and m EHC = (x + 80), find x. 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 Which is an equation of the line that passes through the point ( 2, 4) and is parallel to the line y = 3? A. x = 2 B. y = 2 C. x = 4 D. y = In the accompanying diagram, parallel lines AB and CD are cut by transversal GH at E and F, respectively. If m GEB = (2x 30) and m EFD = (x + 15), find the value of x. 62. In the accompanying diagram, AB and CD intersect at E. If m AEC = 2x + 40 and m CEB = x + 20, find 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 AB and CD at G and H, respectively. If m EGB = 2x + 40 and m FHC = 3x 10, what is the value of x? page 10

11 68. As shown in the diagram below, lines m and n are cut by transversal p. 71. The diagram below shows the construction of line m, parallel to line l, through point P. If m 1 = 4x + 14 and m 2 = 8x + 10, lines m and n are parallel when x equals A. 1 B. 6 C. 13 D Which diagram shows a correct mathematical construction using only a compass and a straightedge to bisect an angle? 70. A straightedge and compass were used to create the construction below. Arc 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? A. 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. C. If two lines are perpendicular to the same line, they are parallel. D. If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel. Which statement is false? page 11

12 72. Janet graphed a triangle on the coordinate grid shown. Janet rotated the triangle 90 clockwise about the origin to create figure A B C. What are the coordinates of the vertices of the figure A B C after the rotation? page 12