Geometry Summative Review 2008

Geometry Summative Review 2008 Page 1 Name: ID: Class: Teacher: Date: Period: This printed test is for review purposes only. 1. ( 1.67% ) Which equation describes a circle centered at (-2,3) and with radius 5? A. B. C. D. 2. ( 1.67% ) All of the following equations represent lines that are parallel to the equation except A. B. C. D. 3. ( 1.67% ) If the center of a circle is A(0,0) and a point B(4,3) lies on the circle, what is the value of r in the equation of the circle

Page 2 A. 5 B. 25 C. 7 D. 0 4. ( 1.67% ) Suppose and are complementary angles and and. Solve for x and then find m and. A. B. C. D. = 20 and = 65 and = 119 and = 71 and m = 70 = 25 = 61 = 19

Geometry Summative Review 2008 Page 3 Name: ID: 5. ( 1.67% ) In the diagram, and Find the value of x. A. B. C. D. 6. ( 1.67% ) The figure shown is a regular pentagon. Which geometric concept can you use to determine the measure of A. The sum of the exterior angles of a polygon is 360 degrees. B. The sum of a polygon's interior angles is 180 degrees. C. The sum of the exterior angles of a polygon is 180 degrees. D. The sum of each of a polygon's interior and exterior angles is 90 degrees. 7. ( 1.67% ) An equilateral triangle is also

Page 4 A. an obtuse triangle. B. a right triangle. C. an isosceles triangle. D. a scalene triangle. 8. ( 1.67% ) A quadrilateral has one pair of opposite sides that are congruent. The other pair of opposite sides are parallel. What do you know about the shape of the quadrilateral? A. The quadrilateral is a parallelogram. B. There is not enough information to determine the shape of the quadrilateral. C. The quadrilateral is an isosceles trapezoid. D. The quadrilateral is a rectangle.

Geometry Summative Review 2008 Page 5 Name: ID: 9. ( 1.67% ) A construction worker needs to lay triangular tiles in the pattern shown. If the pattern continues, what transformations might she use to move triangle B to the next position in the pattern? A. dilation and translation B. reflection and dilation C. rotation of 90 and reflection D. reflection and translation 10. ( 1.67% ) Jonas drew four different convex polygons: a triangle, a quadrilateral, a pentagon, and an octagon. He then measured and labeled the angles as shown. Using his figures, which of the following conjectures about the sum of the interior angles of an n-sided polygon is true? A. The sum of the interior angles of an n-sided polygon is equal to 360 degrees. B. The sum of the interior angles of an n-sided polygon is equal to degrees. C. The sum of the interior angles of an n-sided polygon is equal to degrees. D. The sum of the interior angles of an n-sided polygon is equal to degrees. 11. ( 1.67% )

Page 6 If and? what is the value of x A. 58 B. 49.5 C. 22 D. -22 12. ( 1.67% ) Which is the correct reason for statement 1 in the proof? A. Addition Property B. Linear Pair Postulate C. Substitution Property D. Given E. None of the above.

Geometry Summative Review 2008 Page 7 Name: ID: 13. ( 1.67% ) A student connects points on a coordinate grid. and The student thinks that side might be perpendicular to side Which formula could the student use to justify this statement? A. The distance formula: B. The formula for a triangle's area: C. The slope formula: D. The midpoint formula: 14. ( 1.67% ) A circle has the center K. A triangle, What must be true about this triangle? is formed in the circle by chord and the radii and A. B. C. D. must be a scalene triangle. must be an equilateral triangle. must be an isosceles triangle. must be a right triangle. 15. ( 1.67% )

Page 8 Which statement is supported by the information shown in the figure? A. B. C. D. 16. ( 1.67% ) Given: and are right angles. Is the statement true, and if so, by which postulate? A. Yes, by SAS. B. Yes, by SSS. C. No, they are not congruent. D. Yes, by ASA.

Geometry Summative Review 2008 Page 9 Name: ID: 17. ( 1.67% ) Which of the following statements must be true in order to prove that a quadrilateral is a parallelogram? A. The diagonals of the quadrilateral bisect the angles. B. The diagonals of the quadrilateral are perpendicular. C. The diagonals of the quadrilateral bisect each other. D. The diagonals of the quadrilateral are congruent. 18. ( 1.67% ) The following proof has three missing statements. Given: is parallel to Prove: N is the midpoint of and Statements (Reasons) 1 is parallel to and (Given) 2 (Vertical Angles) 3?? 4?? 5?? 6 N is the midpoint of (Definition of a midpoint) The missing statements are listed below, but they are out of order. Statement R: Statement S: (Angle-Side-Angle (Alternate Interior Angles) ) Statement T: ) (Corresponding Parts of What is the correct order for these statements to be placed in the proof above? A. Statement S, Statement T, Statement R B. Statement S, Statement R, Statement T C. Statement R, Statement T, Statement S D. Statement R Statement S, Statement T

Page 10 19. ( 1.67% ) The measure of the supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement. A. 26 and 64 B. 60 and 120 C. 56 and 124 D. 64 and 116 E. 34 and 56 20. ( 1.67% ) Triangle ABC is to be enlarged through a dilation centered at the origin with a scale factor of 2 to create All of the following correctly represent this dilation except A. A graphical representation of the triangles: B. A symbolic representation of the ratios: C. A tabular representation of the coordinates: D. A tabular representation of the side lengths:

Page 11 Geometry Summative Review 2008 Name: ID: 21. ( 1.67% ) In circle F,? and. What is the value of A. 45º B. 60º C. 90º D. 75º E. 135º 22. ( 1.67% ) Figure J'K'L'M'N' is a dilation of figure JKLMN. What scale factor was used to create the dilation? A. B. C. D.

Page 12 23. ( 1.67% ) In parallelogram QRST, the length of is 180 units, and the is 100 units. length of All of the following can be found using this information except A. The perimeter of parallelogram QRST B. The area of parallelogram QRST C. The length of D. The measure of 24. ( 1.67% ) The diagram shows a pattern of regular polygons with 3, 4, 5, and 6 sides. Inside each polygon, segments are drawn from the center to the vertices, forming congruent central angles in each polygon. What would be the measure of the central angle formed inside a regular decagon, which has 10 sides? A. 54º B. 45º C. 36º D. 40º

Geometry Summative Review 2008 Page 13 Name: ID: 25. ( 1.67% ) In the figure, angle Q measures 70º, and bisects What is the measure of A. 20º B. 30º C. 40º D. 70º 26. ( 1.67% ) The measure of each interior angle of a regular octagon is 135º. When the diagonals are drawn from one vertex of the octagon, six triangles are formed, each with at least one 22.5º angle. The three angles in these triangles could have any of the following sets of measures EXCEPT. A. 22.5º, 22.5º, and 135º B. 22.5º, 78.75º, and 78.75º

Page 14 C. 22.5º, 45º, and 112.5º D. 22.5º, 67.5º, and 90º 27. ( 1.67% ) All of these triangles are similar to the one shown except - A. B. C.

Page 15 D. 28. ( 1.67% ) In the figure, is isosceles with a vertex angle of 30º. If bisects and bisects then which of these best describes A. Acute triangle B. Acute isosceles triangle C. Right triangle D. Right isosceles triangle.

Page 16 Geometry Summative Review 2008 Name: ID: 29. ( 1.67% ) Which figure in the diagram is a rotation of figure 1? A. Figure 2 B. Figure 3 C. Figure 4 D. Figure 5 30. ( 1.67% ) An editor wants to insert a graphic for the word "NEWS" into a document, as shown. What composition of transformations could be used to place this image into the document as desired? A. Reflection, then translation B. Reflection, then rotation C. Dilation, then rotation D. Dilation, then translation 31. ( 1.67% )

Page 17 If the isosceles trapezoid is reflected over the x-axis and then translated 4 units left and 5 units down, the coordinates of the reflected trapezoid will include - A. (-5,3), (-3,3), and (0,3) B. (-1,-2), (1,-2), and (-4,2) C. (-1,2), (-4,2), and (4,-2) D. (-5,-7), (-3,-7), and (-8,-3) 32. ( 1.67% ) Which of the following shows triangle ABC dilated by a scale factor of -axis? then reflected over the y A. B.

Page 18 C. D.

Geometry Summative Review 2008 Page 19 Name: ID: 33. ( 1.67% ) Consider the figures shown. Which image could result from taking Figure #1, translating it to the right, and then rotating it about point R? A. Figure 2 B. Figure 3 C. Figure 5 D. Figure 6 34. ( 1.67% ) The ladder to the top of a slide is 6 ft long and perpendicular to the ground. If the slide makes an angle of 30 with the ground, then what is the approximate length of the slide? A. 14.7 ft B. 10.4 ft C. 12.0 ft D. 8.5 ft 35. ( 1.67% ) The numbers 3, 4, and 5 are called a Pythagorean triple because the numbers satisfy the equation Any common multiples of 3, 4, and 5 will also be a Pythagorean triple. All of the following are Pythagorean triples except

Page 20 A. 15, 20, and 25 B. 36, 48, and 60 C. 75, 100, and 125 D. 18, 30, and 42 36. ( 1.67% ) For a car to travel over Daniel's Peak, it would have to drive 2.6 kilometers to the top at a 30º angle of elevation, then go 2.6 kilometers down the other side at a 30º angle of depression. A road crew is considering constructing a tunnel that goes from one side of Daniel's Peak to the other, directly through the base of the mountain (or, from point B to point D). About how many kilometers could be saved by driving through such a tunnel instead of traveling over the top of the peak? A. 0.7 km B. 0.9 km C. 1.3 km D. 1.5 km

Geometry Summative Review 2008 Page 21 Name: ID: 37. ( 1.67% ) A plane flies above the ocean and sights a boat in the water at a 30º angle of depression. The plane is currently 2000 yards above the water. What is the horizontal distance to the nearest yard from the plane to the boat? A. 2000 yds B. 3000 yds C. 4000 yds D. 3464 yds 38. ( 1.67% ) Cheryl wants to create a rectangular garden with a path joining the opposite corners. The diagonal path forms a 30º angle with the side of the garden. If the shortest side of the rectangular garden is 20 feet long, how many feet long will the diagonal path be? A. 40 feet B. 25 feet C. 35 feet

Page 22 D. 45 feet 39. ( 1.67% ) in the coordinate plane has endpoints with coordinates true? (2,4) and (8,12). Which of the following is A. The perpendicular bisector of B. The perpendicular bisector of C. The perpendicular bisector of D. The perpendicular bisector of has slope has slope has slope has slope and contains point and contains point and contains point and contains point (5,8). (5,8). (8,5). (8,5). 40. ( 1.67% ) The corners for a fence are located at A (11,3), B (3,-11), C (-13,-9), and D (-5,9). Which of the following best describes the shape of the fence? A. Square B. Rectangle C. Rhombus D. Trapezoid E. Quadrilateral

Geometry Summative Review 2008 Page 23 Name: ID: 41. ( 1.67% ) Which of the following are all of the distinct line segments that are formed on the ant's skating surface? A. AB, AC, CB B. AB, AC, CB, BA, CA, BC C. AC, CB D. AB, AC 42. ( 1.67% ) Which of the named angles is not an angle found in the picture? A. B. C. D. 43. ( 1.67% ) Which is an equation of a line parallel to -intercept of 1? that has a y A.

Page 24 B. C. D. 44. ( 1.67% ) Which graph best represents a line parallel to the line with the equation A. B. C. D.

Geometry Summative Review 2008 Page 25 Name: ID: 45. ( 1.67% ) Two perpendicular lines have the equations second equation? and, of the What is the slope, m A. B. C. D. 46. ( 1.67% ) At Piggy's Pizza, a Giant pizza is 18 inches in diameter. What is the area of this pizza? A. B. C. D. 47. ( 1.67% ) On their Giant (18") pizza, Piggy's prepares a -inch ring of crust around the outside. What is the total area of this ring of crust? A. B.

Page 26 C. D. E. 48. ( 1.67% ) What is the area of this trapezoid in square units? A. 96 square units B. 120 square units C. 128 square units D. 160 square units

Geometry Summative Review 2008 Page 27 Name: ID: 49. ( 1.67% ) The figure shows a parallelogram, a triangle, a rectangle, and a trapezoid. According to the dimensions given, which of the shapes has the least area? A. Parallelogram B. Triangle C. Trapezoid D. Rectangle 50. ( 1.67% ) A telephone pole set perpendicular to the ground is 24 feet tall. A support cable is attached to the top of the pole to keep the pole from leaning. The stake for the cable is set in the ground 18 feet away from the base of the pole, as shown. How long is the support cable? A. 54 ft B. 30 ft C. 27 ft D. 6 ft

Page 28 51. ( 1.67% ) The Bermuda Triangle has vertices at Bermuda, Miami, and San Juan. An altitude with 1120 miles is dropped from Bermuda. The bottom of the altitude is 445 miles from Miami. What is the distance from Bermuda to Miami? A. 1027 miles B. 1565 miles C. 1205 miles D. 675 miles 52. ( 1.67% ) Circle C has diameter that is perpendicular to chord, as shown. at point X If the chord length and the diameter then A. 2 B. 2.5 C. 3 D. 4

Geometry Summative Review 2008 Page 29 Name: ID: 53. ( 1.67% ) Using the measurements given in the diagram of the circle, what is the value of x? A. 65º B. 70º C. 35º 54. ( 1.67% ) Given what is A. 140º B. 70º C. 220º 55. ( 1.67% )

Page 30 is isosceles, where If and then find A. 10º B. 80º C. 20º D. 180º 56. ( 1.67% ) If then find A. 40º B. 120º C. 70º D. 140º

Geometry Summative Review 2008 Page 31 Name: ID: 57. ( 1.67% ) The figure shows trapezoid ABCD, which is similar to trapezoid FGCE. What is the length of AB? A. 15 units B. 16 units C. 18 units D. 21 units 58. ( 1.67% ) An art supply store keeps all sizes of frames in stock. If you wanted to frame an 8 in. x 10 in. photo in a frame that is larger, but similar, which of the following frame sizes would you use? A. 12 in. x 15 in. B. 14 in. x 16 in. C. 16 in. x 18 in. D. 28 in. x 38 in. 59. ( 1.67% ) A surveyor has taken some measurements on a trapezoid-shaped lot that runs next to Main Street. What is the area of this lot?

Page 32 A. 4638 square yards B. 4608 square yards C. 3744 square yards D. 2928 square yards E. 2880 square yards 60. ( 1.67% ) A park ranger has a scope up to her eye and is looking at a giraffe 27 feet away. If the scope is 9 inches long with a diameter of 6 inches, and the giraffe's image fills the scope, how tall is the giraffe? A. 40.5 feet B. 9 feet C. 2 feet D. 18 feet

Page 33 Geometry Summative Review 2008 Geometry Summative Review 2008 Printed Question Order Reported As Question Number Question Number in Pool Question Weight 1 1 124 1.67% 2 2 346 1.67% 3 3 1487 1.67% 4 4 48 1.67% 5 5 65 1.67% 6 6 538 1.67% 7 7 1513 1.67% 8 8 1071 1.67% 9 9 537 1.67% 10 10 1024 1.67% 11 11 1816 1.67% 12 12 60 1.67% 13 13 592 1.67% 14 14 593 1.67% 15 15 932 1.67% 16 16 1842 1.67% 17 17 555 1.67% 18 18 931 1.67% 19 19 50 1.67% 20 20 785 1.67% 21 21 128 1.67% 22 22 395 1.67% 23 23 403 1.67% 24 24 1018 1.67% 25 25 1514 1.67% 26 26 1518 1.67% 27 27 1737 1.67% 28 28 1933 1.67% 29 29 53 1.67% 30 30 918 1.67% 31 31 1768 1.67%

Page 34 32 32 1770 1.67% 33 33 1919 1.67% 34 34 777 1.67% 35 35 779 1.67% 36 36 1686 1.67% 37 37 1736 1.67% 38 38 1778 1.67% 39 39 58 1.67% 40 40 120 1.67% 41 41 1814 1.67% 42 42 1815 1.67% 43 43 63 1.67% 44 44 414 1.67% 45 45 496 1.67% 46 46 140 1.67% 47 47 141 1.67% 48 48 1951 1.67% 49 49 1953 1.67% 50 50 79 1.67% 51 51 1291 1.67% 52 52 1526 1.67% 53 53 126 1.67% 54 54 130 1.67% 55 55 1505 1.67% 56 56 1507 1.67% 57 57 1703 1.67% 58 58 1793 1.67% 59 59 1694 1.67% 60 60 1993 1.67%