# Geometry EOC Practice Test #3

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1 Class: Date: Geometry EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which regular polyhedron has 12 petagonal faces? a. dodecahedron b. tetrahedron c. icosahedron d. cube 2. Melissa used a compass and a ruler to construct two parallel lines and a transversal. Which of the following statements is a conjecture that Melissa can make about the angles formed by the parallel lines and the transversal. a. Pairs of same side interior angles are congruent. b. Pairs of alternate interior angles are congruent. c. Pairs of alternate exterior angles are supplementary. d. Pairs of corresponding angles are complementary. 3. Which equation defines the circle in the graph? a. (x + 3) 2 + (y 2) 2 = 25 c. (x 3) 2 + (y + 2) 2 = 18 b. (x + 3) 2 + (y 2) 2 = 18 d. (x 3) 2 + (y + 2) 2 = 25 1

2 4. The net below represents an icosahedron. How many faces does an icosahedron have? a. 10 b. 12 c. 15 d A tourist is standing at point T in the following diagram. The tourist wants to go to the nearest restroom facility. Which of the following statements is correct? a. Restroom facility R is closer. b. Restroom facility S is closer. c. Both restroom facilities are the same distance from the tourist. d. The only distance that can be determined correctly is RS. 2

3 6. What is the midpoint of PQ? a. (1, 4) b. (0, 4) c. (0, 3) d. (1, 3) 7. When writing a coordinate proof, which of the following would you use to prove that the diagonals of a quadrilateral are congruent? a. the slope formula c. the point-slope formula b. the distance formula d. the midpoint formula 8. mde = 128 and mbc = 63. What is m A? a b. 65 c d

4 9. What is the converse of the statement below? If today is Friday, then tomorrow is Saturday. a. If tomorrow is not Saturday, then today is not Friday. b. If today is Saturday, then tomorrow is not Friday. c. If tomorrow is Saturday, then today is Friday. d. If today is not Friday, then tomorrow is not Saturday. 10. Find the area of a regular hexagon with side length 6 m. Round to the nearest tenth. a m 2 b. 54 m 2 c m 2 d m 2 4

5 11. In the figure below, p Ä q. Which of these statements is NOT true? a. m 1 = m 4 c. m 6 + m 3 = 180 b. m 6 = m 2 d. m 2 + m 5 = The dimensions of a rectangle are multiplied by a factor of 2 to form a new rectangle. Which of the following best describes the relationship between the perimeter of the old rectangle and the perimeter of the new rectangle? a. The perimeter of the new rectangle is c. The perimeter of the new rectangle is half the original rectangle. b. The perimeter of the new rectangle is twice the original rectangle. four times the original rectangle. d. The perimeter of the new rectangle is one-fourth the original rectangle. 5

6 13. Nancy is covering a wall in her attic with wallpaper. The wall is trapezoid-shaped with top and bottom bases of 15 feet and 22 feet. The height of the wall is 8 feet. How much wallpaper will she need to cover the wall? a. 296 square feet b. 148 square feet c. 102 square feet d. 78 square feet 14. The picture below represents a 20-foot-tall flagpole that casts a 16-foot-long shadow. The dashed line in the figure represents the point where the shadow ends to the top of the flag. What is the approximate angle of elevation formed by the ground and the dashed line? a. 37 b. 39 c. 51 d. 53 6

7 15. Find the surface area to the nearest tenth. a units 2 b units 2 c units 2 d units Adrian constructed 3 parallel lines as part of an art project. He also drew a line passing through each of the parallel lines. Some of the angles formed by the intersection of line t and lines l, m, and n are numbered in the diagram below. Which conjecture can Adrian make about the angles formed by line t and lines l, m, and n? a. Angles 2, 3, and 4 are congruent. b. Angles 1 and 3 are supplementary. c. Angles 2 and 4 are congruent. d. Angles 4 and 6 are supplementary. 17. Suppose you want to build a mirror with the frame shown. The outer edges of the frame form a regular polygon. What is the measure of y? a. 144 b. 120 c. 60 d. 36 7

8 18. Look at parallelogram ABCD below. How could you prove that ABCD is a rhombus? a. Show that the diagonals are perpendicular. c. Show that both pairs of opposite angles are congruent. b. Show that the diagonals are congruent. d. Show that two pairs of opposite sides are congruent. 19. Stephanie collects snow globes. The snow globes come in cube-shaped boxes as shown below. How does the change in the length of the sides from the smaller cube to the larger cube affect the surface area? a. The surface area increases by a factor of 2. b. The surface area increases by a factor of 2.5. c. The surface area increases by a factor of d. The surface area increases by a factor of

9 20. In the figure below, NP is the altitude drawn to the hypotenuse of MNO. If MP = 16 and PO = 4, what is the length of the altitude? a. 6 b. 8 c. 9 d Four shaded circles, each of radius 8 centimeters, are packed in a square as shown. Which expression, in square centimeters, represents the area that is NOT shaded inside the square? a. 32(32) π(8) 2 c. 16(16) 4π(8) 2 b. 4π(8) 2 32(32) d. 32(32) 4π(8) 2 9

10 22. Given: BD and AE intersect at point C, point C is the midpoint of BD, point C is the midpoint of AE. Which can be used to prove ABC EDC? a. ASA c. SAS b. SSS d. AAA 23. What is the value of x for the similar polygons? a. x = 11 2 c. x = 9 b. x = 8 d. x = The coordinates of endpoint D in CD are at D(5, 5). If the midpoint of the segment is at M(1, 1), what are the coordinates of point C? a. (3, 2) b. ( 3, 7) c. ( 2, 6) d. ( 3, 8) 10

11 25. The junior league baseball diamond at a playground is a square with sides that measure 65 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth. a feet b. 130 feet c. 65 feet d. 8,450 feet 26. What is the measure of arc AB? a. 40 c. 110 b. 100 d

12 27. Which statement is NOT true about the figure? a. It has 6 vertices. b. It has 8 edges. c. It has 5 faces. d. It is a triangular prism. 28. Three angles of quadrilateral ABCD have measures 68, 97, and 112. What is the value of x? a. 7 b. 83 c. 97 d A square-based prism has a cylindrical hole bored through the middle as shown in the diagram below. What is the approximate remaining volume of the prism? Use 3.14 for π. a cubic centimeters c cubic centimeters b cubic centimeters d. 1,052 cubic centimeters 12

13 30. Which equation defines the circle with center (5, 4) and radius 3? a. ( x 5) + Ê ËÁ y + 4 ˆ 2 = 9 c. ( x + 4) + Ê ËÁ y 5 ˆ 2 = 3 b. ( x + 5) + Ê ËÁ y 4 ˆ 2 = 9 d. ( x + 5) + Ê ËÁ y 4 ˆ 2 = Quadrilateral CDEF has vertices C(8, 2), D(7, 4), and E(1, 5). What are the coordinates of vertex F if CDEF is a parallelogram? a. (2, 2) c. (2, 1) b. (1, 1) d. (3, 3) 32. In the diagram below, m M = 44º and MN = 12 yards. What is the length of MP to the nearest tenth? a. 8.6 yards c. 17 yards b yards d yards 33. What is sin D in the right triangle shown below? Express your answer as a fraction in lowest terms. a. b. c. d

14 34. Figure ABCD is shown below on the coordinate plane. Which of the following transformations will produce an image with a vertex at (1, 1)? a. Translate figure ABCD 2 units to the right and 2 units down. c. Reflect figure ABCD across the y-axis. b. Reflect figure ABCD across the x-axis. d. Translate figure ABCD 4 units to the right and 2 units up. 35. Complete this statement: For parallelogram WXYZ, XO?. What definition or theorem justifies your answer? a. WO; the diagonals of a parallelogram bisect each other. b. ZO; the diagonals of a parallelogram bisect each other. c. YO; the diagonals of a parallelogram bisect each other. d. WZ; the diagonals of a parallelogram bisect each other. 14

15 36. For what value of x is a Ä b? a. 17 c. 33 b. 21 d The figure shown is a kite. What is the y-coordinate of point D? a. s c. 2s + 5 b. 2 d. s

16 38. The base of a 12-foot ladder is 5 feet from a building. To the nearest degree, what angle does the ladder make with the ground? a. 23 b. 25 c. 65 d A landowner wants to find the distance d across a pond. The two overlapping right triangles shown are similar. Using the measurements shown, what is d? a. 36 meters c. 96 meters b. 76 meters d. 124 meters 40. Corey is 66 inches tall. At noon, Corey casts a shadow 108 inches long. At the same time, a tree casts a shadow 216 inches long. The right triangle formed by Corey and his shadow is similar to the right triangle formed by the tree and its shadow. How tall is the tree? a. 132 inches c. 153 inches b. 145 inches d. 160 inches 16

17 41. What is the correct order of the sides of the triangle from longest to shortest? a. LN, LM, MN c. LN, MN, LM b. LM, MN, LN d. MN, LN, ML 42. What is a rule that describes the translation QRST Qʹ Rʹ S ʹ T ʹ? a. (x,y) (x 6,y + 2) c. (x,y) (x 2,y + 6) b. (x,y) (x + 6,y 2) d. (x,y) (x + 2,y 6) 17

18 43. If parallelogram WXYZ shown below is rotated 180 about the origin to create image W'X'Y'Z', which of the following is NOT true? a. m W = m W ' c. m X '+ m W '= 180 b. Y 'Z '= 7 d. X 'Y '> XY 44. How do you write the contrapositive of the conditional statement below? If m 1 = 60, then 1 is acute. a. If m 1 = 60, then 1 is not acute. b. If 1 is not acute, then m c. If 1 is acute, then m 1 = 60. d. If m 1 60, then 1 is not acute. 45. How many two inch cubes will fit inside the four inch cubic box? a. 4 b. 6 c. 8 d

19 46. Francesco built a box to store his baseball cards. The box is shown below. Francesco needed more storage and built a similar box that was one-half of each the length, the width, and the height of the first box. By what factor does the change in dimension between the two boxes affect the volume? a. The volume of the smaller box is b. The volume of the smaller box is of the volume of the larger box. of the volume of the larger box. c. The volume of the smaller box is 1 4 d. The volume of the smaller box is 1 2 of the volume of the larger box. of the volume of the larger box. 47. If ΔMNO ΔPQR, which of the following can you NOT conclude as being true? a. MN PR c. NO QR b. M P d. N Q 48. The sum of the measures of the interior angles of a convex polygon is Classify the polygon by its number of sides. a. hexagon b. septagon c. nonagon d. 14-gon 49. What is the inverse of the statement below? If you live in Tallahassee, then you live in Florida. a. If you do not live in Florida, then you do not live in Tallahassee. b. If you do not live in Florida, then you live in Tallahassee. c. If you do not live in Tallahassee, then you do not live in Florida. d. If you live in Florida, then you live in Tallahassee. 19

20 50. In this drawing, line p is parallel to line j and line t is perpendicular to AB. What is the measure of BAC? a. 128 b. 118 c. 38 d What word best completes the following sentence? A conditional statement can have a of true or false. a. hypothesis c. counterexample b. truth value d. conclusion 52. Each unit on the map represents 5 miles. What is the best estimate of the distance from Oceanfront to Seaside? a. about 8 miles c. about 39 miles b. about 10 miles d. about 50 miles 20

21 53. What is the volume of the figure below? a. 215 cubic inches c. 190 cubic inches b. 200 cubic inches d. 175 cubic inches 54. Which coordinates are the vertices of a figure that is similar to the figure pictured below? a. ( 2a, 0), (0, 2c), (2b, 0), (0, 2c) c. ( a + 1, 0), (1, c), (b, 1), (0, c + 1) b. ( 1 2 a,0),(0, 1 c),(2b,0),(0,2c) d. (2a, 0), (0, 4c), ( 2b, 0), (0, 2c) 2 21

22 55. The net below represents a regular polyhedron. How many vertices does the figure have? a. 6 b. 7 c. 8 d. 9 22

23 Geometry EOC Practice Test #3 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 STA: MA.912.G ANS: B PTS: 1 DIF: Moderate REF: Geom: 2-1, 2-2, 3-1, 3-2 STA: MA.912.G ANS: D PTS: 1 STA: MA.912.G ANS: D PTS: 1 DIF: Low REF: Geom: 1-7, 1-7 Extend STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: D PTS: 1 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Low REF: Geom: 2-3 STA: MA.912.D ANS: C PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: B PTS: 1 DIF: Low REF: Geom: 11-2 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.T ANS: C PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Moderate REF: Geom: 2-1, 2-2, 3-1, 3-2 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Low REF: Geom: 12-4 STA: MA.912.G ANS: B PTS: 1 DIF: Moderate REF: Geom: 5-2 STA: MA.912.G ANS: D PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Moderate REF: Geom: 4-3, 4-4, 4-5 STA: MA.912.G.4.6 MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 DIF: Moderate REF: Geom: 1-3 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Moderate REF: Geom: 6-1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G.6.6 1

24 31. ANS: C PTS: 1 DIF: High REF: Geom: 6-2 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.T ANS: B PTS: 1 DIF: Moderate REF: Geom: 8-4 STA: MA.912.T ANS: C PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: D PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.T ANS: C PTS: 1 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.G ANS: D PTS: 1 DIF: Low REF: Geom: 9-3 STA: MA.912.G ANS: B PTS: 1 DIF: Low REF: Geom: 2-3 STA: MA.912.D ANS: C PTS: 1 STA: MA.912.G ANS: B PTS: 1 DIF: Moderate REF: Geom: 12-6 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: C PTS: 1 STA: MA.912.G ANS: C PTS: 1 DIF: Low REF: Geom: 2-3 STA: MA.912.D ANS: C PTS: 1 DIF: Moderate REF: Geom: 3-1, 3-2 STA: MA.912.G ANS: B PTS: 1 STA: MA.912.D ANS: C PTS: 1 STA: MA.912.G ANS: D PTS: 1 STA: MA.912.G ANS: A PTS: 1 STA: MA.912.G ANS: A PTS: 1 DIF: Low REF: Geom: 1-7, 1-7 Extend STA: MA.912.G.7.1 2

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