Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain

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1 AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 )

2 1. Amy drew a circle graph to represent the ages of people who were surveyed for a consumer group. Of those surveyed, 30% were over the age of 65. Which one of the following graphs best represents the survey results? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (2 of 36 )

3 2. A square has two sides on the lines and It has a vertex at What is the perimeter, in units, of the square? Jennifer keeps a box under her bed to store clothes. The box is in the shape of a rectangular prism as shown in the figure below Jennifer's sister, Molly, made a box that had the same height as Jennifer's box. Molly, however, realized that she could triple the length and double the width and it would still fit under her bed. What is the ratio of the volume of Molly's box to the volume of Jennifer's box? 6:1 12:1 36:1 216:1 4. Which number is closest to the value ofxin the figure below? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (3 of 36 )

4 In the figures shown below, is similar to. What is the length of? 2.0 cm 4.5 cm 12.5 cm 22.5 cm 6. Parallelogram is shown in this diagram. Line segments are diagonals of parallelogram Point Jis the midpoint of Point Kis the midpoint of Point Lis the midpoint of Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (4 of 36 )

5 Point Mis the midpoint of Line segment is 12 centimeters long. What is the length of 6 cm 7 cm 8 cm 9 cm 7. Parallelogram is shown in this diagram. Line segments are diagonals of parallelogram Point Jis the midpoint of Point Kis the midpoint of Point Lis the midpoint of Point Mis the midpoint of The perimeter of parallelogram is 44 centimeters. What is the length of 5 cm 5.5 cm 10 cm 10.5 cm Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (5 of 36 )

6 8. In the figures shown below, is similar to. What is the length of? 2.0 cm 4.5 cm 12.5 cm 22.5 cm 9. In the triangle below, which list shows the angles from smallest to largest? 10. The sine of in this figure is Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (6 of 36 )

7 Which equation must be true? 11. This triangle has the measures shown. Which measures shown in the triangle are equivalent to 12. The tangent of in this diagram is Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (7 of 36 )

8 The height of the mountain, z, is 1400 feet. Which equation must be true? 13. This diagram shows similar right triangles. Which equation must be true? 14. This is a right triangle. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (8 of 36 )

9 Which expression is equivalent to 15. The tangent of in this triangle is Which equation must be true? 16. The measure of in right is Which equation must be true? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (9 of 36 )

10 17. Angles 1, 2, 3, and 4 are marked in these similar right triangles. Which measure is equivalent to 18. What is the value ofxin the triangle below? 19. Use this diagram and information to answer the question. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (10 of 36 )

11 In the diagram, PQRS is a kite. = 24 inches = 36 inches What is the length, to the nearest 0.01 inch, of 9.58 inches inches inches inches 20. Use this diagram and information to answer the question. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (11 of 36 )

12 Which is the best estimate of the ratio 21. This diagram shows the lengths of each side of a kite. What is the value of w, to the nearest inch? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (12 of 36 )

13 10 in 20 in 30 in 40 in 22. The angle of depression from a helicopter to the top of a monument is 16, as shown in this diagram. How far above the ground, to the nearest yard, is the helicopter? 798 yd. 828 yd yd yd. 23. A bridge is built across a stream as shown in this diagram. The top of the bridge is 4 meters above the stream. Which equation can be used to find x, the length, in meters, of the bridge? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (13 of 36 )

14 24. A building casts a 50-foot shadow. The angle of elevation from the end of the shadow to the top of the building is 69. What is the height, to the nearest foot, of the building? 19 ft. 47 ft. 54 ft. 130 ft. 25. Chords and are equidistant from center P in this circle. Chord is 6 units long. Which statement MUST be true about the value of x? It is 1.5. It is between 1.5 and 4.5. It is 4.5. It is greater than 4.5. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (14 of 36 )

15 26. The center of circle P is located at as shown on this coordinate plane. Line m is tangent to circle P at What is the equation of line m? 27. Circle O is inscribed inside quadrilateral PRST, as shown in this diagram. is tangent to circle O at point Q. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (15 of 36 )

16 What is the perimeter of quadrilateral 80 in. 74 in. 68 in. 54 in. 28. The measure of is in this circle. The measure of is What is the measure of 29. Segments KJ and KL are tangent to circle P. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (16 of 36 )

17 What is the measure of 30. This diagram shows circle P with What is the measure of 31. Points N, P, and Q lie on circle O, as shown in this diagram. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (17 of 36 )

18 The measure of What is the measure of 32. Chord is congruent to chord in circle O, as shown. What is the value of x? Beth made the following pie graph to represent her monthly budget. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (18 of 36 )

19 What percentage of her budget does she spend on her rent and car combined? 50% 72% 90% 180% 34. In the figure below,ois the center of the circle. If the measure of minor arc is 60, what is the measure ofý ABO? A sector of a circle is created from a central angle with a measure of 60. If the diameter of the circle is 6 inches, what is the area of the sector? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (19 of 36 )

20 36. Regular pentagon DEFGH is inscribed in circle P, as shown. The length of is8pyards. Which equation must be true? 37. A new flower bed outside of a town hall is in the shape of a triangle. Two of the side lengths are and Which expression represents a possible length of the third side of the triangle? 38. Triangle the measures of its angles, and two of its side lengths are shown in this diagram. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (20 of 36 )

21 Which expression could represent the length of 39. In this diagram, contains Which statement MUST be true? 40. In the figure below, the diagonals of parallelogramabcdintersect at (5, 2). Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (21 of 36 )

22 What are the coordinates of pointc? (7, 3) (8, 3) (9, 4) (10, 4) 41. An electric company chose this design for its new logo. What is the sum of the interior angles of the hexagon? 42. The measure of one exterior angle of a regular polygon is What is the sum of its interior angles? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (22 of 36 )

23 43. The exterior angles of a triangle have a ratio. What is the smallest exterior angle of the triangle? 44. This diagram shows the shape of a city park. What is the value of A large picnic table is in the shape of a regular polygon. An interior angle of this table measures How many sides does the picnic table have? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (23 of 36 )

24 46. Which pair of triangles MUST be congruent? 47. In this diagram, bisects Which additional piece of information is NOT sufficient to prove Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (24 of 36 )

25 48. Which set of points is equidistant from the rays that form an angle? perpendicular bisector skew line angle bisector central angle 49. An exercise ball has a volume of 2304pcubic inches. What is the surface area of the ball? 96p sq. in. 192p sq. in. 288p sq. in. 576p sq. in. 50. Which graph shows the relationship between the surface area and the volume of a sphere? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (25 of 36 )

26 51. A trophy is shaped like a large golf ball. The diameter of the trophy is 8 inches. What is the volume of the trophy? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (26 of 36 )

27 52. The surface areas of the sphere and the cube shown in this diagram are the same. What is the approximate volume of thesphere? 1000 cm cm cm cm3 53. This diagram shows a sphere cut in half. The volume of this half of a sphere is 144pcubic centimeters. What is the total surface area of the half of the sphere? 72p 108p 144p 180p 54. The vitamin represented in this diagram is in the shape of a cylinder with a half of a sphere on each end. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (27 of 36 )

28 What is the volume, to the nearest cubic millimeter, of the vitamin? 55. A student used this equation to graph a circle. The student then translated the circle 2 units up and 1 unit to the left. What is the equation of the translated circle? 56. This equation represents a circle that has been graphed on a coordinate plane. What ordered pair represents the center of the circle? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (28 of 36 )

29 57. Which equation represents a circle centered at the point on a coordinate plane? 58. A student made this graph of a circle. Which equation represents the circle? 59. This equation represents a circle. Which statement about the graph of the circle is correct? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (29 of 36 )

30 The circle is centered at and has a radius of 12 units. The circle is centered at and has a radius of 12 units. The circle is centered at and has a radius of 144 units. The circle is centered at and has a radius of 144 units. 60. Which equation of a line is perpendicular to the line given by the equation y = x 6? y = x + 1 y = x + 1 y = x + 1 y = x Which line is parallel to the liney= 2x+ 1? y= -2x+ 1 y= y= 2x+ 3 y= In the coordinate system below, to prove that segment is parallel to segment, which of the following must be shown? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (30 of 36 )

31 The length of is half the length of The slope of equals the slope of The length of equals the length of The length of equals the length of 63. In the diagram, point S lies on segment RT and point P lies on segment QT. If what is the value of y? 64. Sam began a construction with his compass and straightedge. The sketch shows the first steps in his construction. Which construction is illustrated by the sketch? the midpoint of a line segment an angle bisector of an acute angle Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (31 of 36 )

32 a bisector of a given line through a point on the line the line perpendicular to a given line through a given point on the line 65. A circle is centered at and contains the point Which statement can be proven algebraically with the information given? The points and lie on the circle. The perimeter of any isosceles right triangle inscribed in the circle is units. Any right triangle with a vertex at and a hypotenuse that is less than 25 units will fit inside the circle. The sum of the areas of two squares with side lengths of 3 units and 4 units is greater than the area of the circle. 66. A clock is designed in the shape of a regular dodecagon. The perimeter of the dodecagon is 54 cm. By joining every other vertex of the dodecagon, a hexagon is formed. If each side of the hexagon is x cm long, what is the value of x to the nearest hundredth? Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (32 of 36 )

33 Answer Key : : cm 6. 6 cm 7. 5 cm cm Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (33 of 36 )

34 inches in yd ft. 25. It is in % (10, 4) Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (34 of 36 )

35 angle bisector p sq. in cm p Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (35 of 36 )

36 The circle is centered at and has a radius of 12 units. 60. y = x y= 2x The slope of equals the slope of the line perpendicular to a given line through a given point on the line 65. The perimeter of any isosceles right triangle inscribed in the circle is units Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (36 of 36 )

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

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