Name: Class: Date: If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF?


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1 Class: Date: Analytic Geometry EOC Practice Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram below of circle O, chords AB and CD intersect at E. If m AEC = 34 and mac = 50, what is mdb? a. 16 b. 18 c. 68 d In the diagram of ABC shown below, D is the midpoint of AB, E is the midpoint of BC, and F is the midpoint of AC. If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF? a. 24 b. 36 c. 40 d The volume, in cubic centimeters, of a sphere whose diameter is 6 centimeters is a. 12π b. 36π c. 48π d. 288π 1
2 4. In circle O shown below, diameter DB is perpendicular to chord AC at E. If DB = 34, AC = 30, and DE > BE, what is the length of BE? a. 8 b. 9 c. 16 d A circle has the equation ( x 2) 2 + Ê Ë Á y + 3ˆ 2 its center and the length of its radius? = 36. What are the coordinates of a. (2, 3) and 6 b. (2, 3) and 6 c. (2, 3) and 36 d. (2, 3) and Circle O with AOC and ABC is shown in the diagram below. What is the ratio of m AOC to m ABC? a. 1 : 1 b. 2 : 1 c. 3 : 1 d. 1 : 2 7. In circle O, diameter AB intersects chord CD at E. If CE = ED, then CAE is which type of angle? a. straight b. obtuse c. acute d. right 2
3 8. In the diagram below, RT m ABT = 125. and ABC are shown with m A = 60 and What is m ACR? a. 125 b. 115 c. 65 d Triangle ABC is similar to triangle DEF. The lengths of the sides of ABC are 5, 8, and 11. What is the length of the shortest side of DEF if its perimeter is 60? a. 10 b c. 20 d In the diagram below, diameter AB bisects chord CD at point E in circle F. If AE = 2 and FB = 17, then the length of CE is a. 7 b. 8 c. 15 d If ABC JKL RTS, then BC must be congruent to a. JL b. JK c. ST d. RS 3
4 12. In ABC, D is the midpoint of AB and E is the midpoint of BC. If AC = 3x  15 and DE = 6, what is the value of x? a. 6 b. 7 c. 9 d In the diagram of UVW below, A is the midpoint of UV, B is the midpoint of UW, C is the midpoint of VW, and AB and AC are drawn. If VW = 7x  3 and AB = 3x + 1, what is the length of VC? a. 5 b. 13 c. 16 d The sides of a triangle are 8, 12, and 15. The longest side of a similar triangle is 18. What is the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle? a. 2 : 3 b. 4 : 9 c. 5 : 6 d. 25 : 36 4
5 15. In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair. Using only the information given in the diagrams, which pair of triangles can not be proven congruent? a. A b. B c. C d. D 16. As shown in the diagram below, CD is a median of ABC. a. AD DB c. ACD CDB b. AC AD d. BCD ACD 5
6 17. The diagram below shows the construction of line m, parallel to line l, through point P. 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. 18. If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? a. XV b. WX c. VW d. NP 19. Chords AB and CD intersect at point E in a circle with center at O. If AE = 8, AB = 20, and DE = 16, what is the length of CE? a. 6 b. 9 c. 10 d In the diagram of circle O below, chord CD is parallel to diameter AB and mcd = 110. What is the mdb? a. 35 b. 55 c. 70 d
7 21. In the diagram below, AC and AD are tangent to circle B at points C and D, respectively, and BC, BD, and BA are drawn. If AC = 12 and AB = 15, what is the length of BD? a. 5.5 b. 9 c. 12 d In the diagram below of circle O, PC and PD are secants. If mcd = 70 and mab = 20, what is the degree measure of P? a. 25 b. 35 c. 45 d Lines p and q are intersected by line p, as shown below. If m 1 = 7x 36 and m 2 = 5x + 12, for which value of x would p Ä q? a. 17 b. 24 c. 83 d. 97 7
8 24. The volume of a sphere is approximately cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter? a. 2.2 b. 3.3 c. 4.4 d In the diagram below of ACT, BE Ä AT. If CB = 3, CA = 10, and CE =6, what is the length of ET? a. 5 b. 14 c. 20 d In the diagram of ABC and EDC below, AE and BD intersect at C, and CAB CED. Which method can be used to show that ABC must be similar to EDC? a. SAS b. AA c. SSS d. HL 8
9 27. In the diagram below of PRT, Q is a point on PR, S is a point on TR, QS is drawn, and RPT RSQ. Which reason justifies the conclusion that PRT RSQ? a. AA b. ASA c. SAS d. SSS 28. Which statement is logically equivalent to "If it is warm, then I go swimming" a. If I go swimming, then it is warm. b. If it is warm, then I do not go swimming. c. If I do not go swimming, then it is not warm. d. If it is not warm, then I do not go swimming. 29. In the diagram below of parallelogram STUV, SV = x + 3, VU = 2x  1, and TU = 4x  3. What is the length of SV? a. 5 b. 2 c. 7 d. 4 9
10 30. Based on the construction below, which statement must be true? a. m ABD = 1 m CBD c. m ABD = m ABC 2 b. m ABD = m CBD d. m CBD = 1 2 m ABD 31. In the diagram below of AGE and OLD, GAE LOD, and AE OD. To prove that AGE and OLD are congruent by SAS, what other information is needed? a. GE LD c. AGE OLD b. AG OL d. AEG ODL 32. A support beam between the floor and ceiling of a house forms a 90º angle with the floor. The builder wants to make sure that the floor and ceiling are parallel. Which angle should the support beam form with the ceiling? a. 45º b. 60º c. 90º d. 180º 10
11 33. In the diagram below of circle O, chords AD and BC intersect at E, mac = 87, and mbd = 35. What is the degree measure of CEA? a. 87º b. 61º c. 43.5º d. 26º 34. In the diagram below of ACT, D is the midpoint of AC, O is the midpoint of AT, and G is the midpoint of CT. If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG? a. 21 b. 25 c. 32 d
12 35. In the diagram of circle O below, chord CD is parallel to diameter AB and mac = 30. What is mcd? a. 150º b. 120º c. 100º d. 60º 36. The diagram below illustrates the construction of PS P. parallel to RQ through point Which staement justifies this construction? a. m 1 = m 2 b. m 1 = m 3 c. PR RQ d. PS RQ 12
13 37. In the diagram below of circle C, mqt = 140, and m P = 40. What is the mrs? a. 50º b. 60º c. 90º d. 110º 38. Which equation represents circle K shown in the graph below? a. ( x + 5) + Ê Ë Á y 1ˆ b. ( x + 5) + Ê Ë Á y 1ˆ = 3 c. ( x 5) + Ê Ë Á y + 1ˆ = 3 = 9 d. ( x 5) + Ê Ë Á y + 1ˆ = 9 13
14 39. In the diagram of ABC and DEF below, AB DE. A D, and B E. Which method can be used to prove ABC DEF? a. SSS b. SAS c. ASA d. HL 40. In the diagram below of ABC, D is a point on AB, AC = 7, AD = 6, and BC = 18. The length of DB could be a. 5 b. 12 c. 19 d In the diagram below of circle O, chords AEand DC intersect at point B, such that mac = 36 and mde = 20. What is m ABC? a. 56º b. 36º c. 28º d. 8º 14
15 42. In the diagram below of circle O, chords AB and CD intersect at E. If CE = 10, ED = 6, and AE = 4, what is the length of EB? a. 15 b. 12 c. 6.7 d The pentagon in the diagram below is formed by five rays. What is the degree measure of x? a. 72º b. 96º c. 108º d. 112º 44. As shown in the diagram below, CD is a median of ABC. Which statement is always true? a. AD DB c. ACD CDB b. AC AD d. BCD ACD 15
16 45. As shown in the diagram below, AC bisects BAD and B D. Which method could be used to prove ABC ADC? a. SSS b. AAA c. SAS d. AAS 46. In the diagram below, line p intersects line m and line n. If m 1 = 7x and m 2 = 5x + 30, lines m and n are parallel when x equals a b. 15 c d In the diagram below of ABC, AE BE, AF CF, and CD BD. Point P must be the a. centroid b. circumcenter c. incenter d. orthocenter 48. In RST, m R = 58 and m S = 73. Which inequality is true? a. RT < TS < RS c. RT < RS < TS b. RS < RT < TS d. RS < TS < RT 16
17 49. Given that ABCD is a parallelogram, a student wrote the proof below to show that a pair of its opposite angles are congruent. What is the reason justifying that B D? a. Opposite angles in a quadrilateral are congruent. b. Parallel lines have congruent corresponding angles. c. Corresponding parts of congruent triangle are congruent. d. Alternate interior angles in congruent triangles are congruent. 50. What is an equation of the circle shown in the graph below? a. ( x 3) + Ê Ë Á y 4ˆ b. ( x + 3) + Ê Ë Á y + 4ˆ = 25 c. ( x 3) + Ê Ë Á y 4ˆ = 10 = 25 d. ( x + 3) + Ê Ë Á y + 4ˆ = 10 17
18 51. In the diagram of KLM below,m L = 70, m M = 50, and MK is extended through N. What is the measure of KLN? a. 60º b. 120º c. 180º d. 300º 52. Which diagram shows the construction of the perpendicular bisector of AB? a. c. b. d. 53. The volume of a rectangular prism is 144 cubic inches. The height of the prism is 8 inches. Which measurements, in inches, could be the dimensions of the base? a. 3.3 in by 5.5 in c. 12 in by 8 in b. 2.5 in by 7.2 in d. 9 in by 9 in 18
19 54. What is the measure of each interior angle of a regular hexagon? a. 60º b. 120º c. 135º d. 270º 55. When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent? a. supplementary angles c. adjacent angles b. linear pair angles d. vertical angles 56. In the diagram below of circle O, diameter AB is parallel to chord CD. If mcd = 70, what is mac? a. 110º b. 70º c. 55º d. 35º 57. In the diagram below, EF is the median of trapezoid ABCD. If AB = 5x  9, DC = x + 3, and EF = 2x + 2, what is the value of x? a. 5 b. 2 c. 7 d The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch? a in 3 b in 3 c in 3 d. 14,137.2 in 3 19
20 59. In the diagram below of ABC, D is the midpoint of AB, and E is the midpoint of BC. If AC = 4x + 10, which expression represents DE? a. x b. 2x + 5 c. 2x + 10 d. 8x A man wants to place a new bird bath in his yard so that it is 30 feet from a fence, f, and also 10 feet from a light pole, P. As shown in the diagram below, the light pole is 35 feet away from the fence. How many locations are possible for the bird bath? a. 1 b. 2 c. 3 d. 0 20
21 61. In the diagram below of circle O, chord AB is parallel to chord CD. Which statement must be true? a. AC BD b. AB CD c. AB CD d. ABD CDB 62. In the diagram below of right triangle ABC, altitude BD is drawn to hypotenuse AC, AC = 16, and CD = 7. What is the length of BD? a. 3 7 b. 4 7 c. 7 3 d The angle formed by the radius of a circle and a tangent to that circle has a measure of a. 45 b. 90 c. 135 d
22 64. In the diagram below, ABC is circumscribed about circle O and the sides of ABC are tangent to the circle at points D, E, and F. If AB = 20, AE = 12, and CF = 15, what is the length of AC? a. 8 b. 15 c. 23 d In the diagram below, AB, BC, and AC are tangents to circle O at points F, E, and D, respectively, AF = 6, CD = 5, and BE = 4. ABC? What is the perimeter of a. 15 b. 25 c. 30 d What is an equation of circle O shown in the graph below? a. ( x + 1) + Ê Ë Á y 3ˆ b. ( x 1) + Ê Ë Á y + 3ˆ = 25 c. ( x 5) + Ê Ë Á y + 6ˆ = 25 = 25 d. ( x + 5) + Ê Ë Á y 6ˆ = 25 22
23 67. In the diagram below of rhombus ABCD, m C = 100. What is the m DBC? a. 40º b. 45º c. 50º d. 80º 68. In the diagram below of circle O, PA is tangent to circle O at A, and PC is a secant with points B and C on the circle. If PA = 8 and PB = 4, what is the length of BC? a. 20 b. 16 c. 15 d
24 69. As shown on the graph below, R' S' T'is the image of RST under a single transformation. Which transformation does this graph represent? a. glide reflection c. rotation b. line reflection d. translation 70. Line n intersects lines l and m, forming the angles shown in the diagram below. Which value of x would prove läm? a. 2.5 b. 4.5 c d In a given triangle, the point of intersection of the three medians is the same as the point of intersection of the three altitudes. Which classification of the triangle is correct? a. scalene triangle c. equilateral triangle b. isosceles triangle d. right isosceles triangle 24
25 72. In the diagram below of ABC, AB AC, m A = 3x, and m B = x What is the value of x? a. 10 b. 28 c. 32 d Scalene triangle ABC is similar to triangle DEF. Which statement is false? a. AB:BC = DE:EF c. ACB DFE b. AC:DF = BC:EF d. ABC EDF 74. In the diagram below, LATE is an isosceles trapezoid with LE AT, LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn. What is the length of LF? a. 6 b. 8 c. 3 d In the diagram below, lines n and m are cut by transversals p and q. What value of x would make lines n and m parallel? a. 110º b. 80º c. 70º d. 50º 25
26 76. What are the center and the radius of the circle whose equation is ( x 5) 2 + Ê Ë Á y + 3ˆ 2 = 16? a. (5, 3) and 16 c. (5, 3) and 4 b. (5, 3) and 16 d. (5, 3) and 4 Short Answer 77. Given: ABC and EDC, C is the midpoint of BD and AE Prove: AB Ä DE Statements Reasons 26
27 78. Given: PA and PB are tangent to circle O, OA and OB are radii, and OP intersects the circle at C. Prove: AOP BOP Statements Reasons 27
28 79. In the diagram below, quadrilateral STAR is a rhombus with diagonals SA and TR intersecting at E. ST = 3x + 30, SR = 8x  5, SE = 3z, TE = 5z + 5, AE = 4z  8, m RTA = 5y 2, and m TAS = 9y + 8. Find SR, RT, and m TAS.. 28
29 80. In the diagram below of GJK, H is a point on GJ, HJ JK, m G = 28, and m GJK = 70. Determine whether answer. GHK is an isosceles triangle and justify your. 29
30 81. Write an equation of the circle whose diameter AB has endpoints A(4, 2) and B(4, 4). [The use of the grid below is optional.]. 30
31 82. Given: AD bisects BC at E. AB BC DC BC Prove: AB DC Statements Reasons 31
32 83. Trapezoid TRAP, with median MQ, is shown in the diagram below. Solve algebraically for x and y.. 32
33 84. In the diagram below, RST is a right triangle. The altitude, h, to the hypotenuse has been drawn. Determine the length of h As shown in the diagram below, the diagonals of parallelogram QRST intersect at E. If QE = x 2 + 6x, SE = x + 14, and TE = 6x 1, determine TE algebraically.. 33
34 86. In circle O shown below, chords AB and CD and radius OA are drawn, such that AB CD, OE AB, OF CD, OF = 16, CF = y + 10, and CD = 4y Determine the length of DF. Determine the length of OA. 87. In the diagram below, ABC DEF, DE = 4, AB = x, AC = x + 2, and DF = x + 6. Determine the length of AB. [Only an algebraic solution can receive full credit.]. 34
35 88. In the diagram below, two parallel lines intersect circle O at points A, B, C, and D, with mab = x + 20 and mdc = 2x 20. Find mab Write an equation of a circle whose center is (3, 2) and whose diameter is Find, in simplest radical form, the length of the line segment with endpoints whose coordinates are (1, 4) and (3, 2) The volume of a cylinder is 12,566.4 cm 3. The height of the cylinder is 8 cm. Find the radius of the cylinder to the nearest tenth of a centimeter.. 35
36 92. In the diagram below of ABC, D is a point on AB, E is a point on BC, AC Ä DE, CE = 25 inches, AD = 18 inches, and DB = 12 inches. Find, to the nearest tenth of an inch, the length of EB In the diagram below, ABC EFG, m C = 4x + 30, and m G = 5x Determine the value of x.. 36
37 94. In the diagram below of right triangle ACB, altitude CD intersects AB at D. If AD = 3 and DB = 4, find the length of CD in simplest radical form A regular pyramid with a square base is shown in the diagram below. A side, s, of the base of the pyramid is 12 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic meters?. 37
38 96. A circle has the equation ( x 3) 2 + Ê Ë Á y + 4ˆ 2 = 10. Find the coordinates of the center of the circle and the length of the circle's radius In the diagram below of HQP, side HP is extended through P to T, m QPT = 6x + 20, m HQP = x + 40, and m PHQ = 4x 5. Find m QPT In the diagram below of circle O, diameter AB is perpendicular to chord CD at E. If AO = 10 and BE = 4, find the length of CE.. 38
39 99. In the diagram below of ABC, DE is a midsegment of ABC, DE = 7, AB = 10, and BC = 13. Find the perimeter of ABC In the diagram below of isosceles trapezoid DEFG, DE Ä GF, DE = 4x  2, EF = 3x + 2, FG = 5x  3, and GD = 2x + 5. Find the value of x.. 39
40 101. Write an equation of the circle graphed in the diagram below The diagram below shows isosceles trapezoid ABCD with AB Ä DC and AD BC. If m BAD = 2x and m BCD = 3x + 5, find m BAD.. 40
41 103. The cylindrical tank shown in the diagram below is to be painted. The tank is open at the top, and the bottom does not need to be painted. Only the outside needs to be painted. Each can of paint covers 600 square feet. How many cans of paint must be purchased to complete the job? In the diagram below of ACD, B is a point on AC such that ADB is an equilateral triangle, and DBC is an isosceles triangle with DB BC. Find m C.. 41
42 Analytic Geometry Answer Section EOC Practice Questions MULTIPLE CHOICE 1. ANS: B 2. ANS: D 3. ANS: B 4. ANS: B 5. ANS: B 6. ANS: B 7. ANS: D 8. ANS: B 9. ANS: B 10. ANS: B 11. ANS: C 12. ANS: C 13. ANS: C 14. ANS: C 15. ANS: A 16. ANS: A 17. ANS: D 18. ANS: A 19. ANS: A 20. ANS: A 21. ANS: B 22. ANS: A 23. ANS: A 24. ANS: A 25. ANS: B 26. ANS: B 27. ANS: B 28. ANS: C 29. ANS: A 30. ANS: B 31. ANS: B 32. ANS: C 33. ANS: B 34. ANS: C 1
43 35. ANS: B 36. ANS: A 37. ANS: B 38. ANS: B 39. ANS: C 40. ANS: B 41. ANS: C 42. ANS: A 43. ANS: C 44. ANS: A 45. ANS: D 46. ANS: B 47. ANS: A 48. ANS: D 49. ANS: C 50. ANS: B 51. ANS: B 52. ANS: A 53. ANS: B 54. ANS: B 55. ANS: D 56. ANS: C 57. ANS: A 58. ANS: B 59. ANS: B 60. ANS: B 61. ANS: A 62. ANS: A 63. ANS: B 64. ANS: D 65. ANS: C 66. ANS: A 67. ANS: A 68. ANS: D 69. ANS: C 70. ANS: B 71. ANS: C 72. ANS: B 73. ANS: D 2
44 74. ANS: A 75. ANS: C 76. ANS: D SHORT ANSWER 77. ANS: Statements 1. C is the midpoint of BD and AE 1. Given Reasons 2. AC EC and DC BC 2. Definition of midpoint 3. ACB ECD 3. Vertical angles are congruent 4. ABC EDC 4. SAS 5. CDE CBA 5. CPCTC 6. CDE and CBA are alternate interior angles 6. Definition of alternatie interior angles 7. AB Ä DE 7. If two lines are cut by a transversal and the alternate interior angles are congruent, the the lines a parallel. 3
45 78. ANS: Statements 1. PA and PB are tangent to circle O, OA and OB are radii, and OP intersects the circle at C 1. Given Reasons 2. OA OB 2. All radii in the same circle are congruent 3. OP OP 3. Reflexive property of congruence 4. OA PA and OB PB 4. Tangents to a circle are perpendicular to a radius at the 5. PAO and PBO are right angles point of tangency 5. Definition of perpendicular lines 6. PAO PBO 6. All right angles are congruent 7. AOP BOP 7. HL 8. AOP BOP 8. CPCTC 79. ANS: SR = 51 RT = 90 m TAS = ANS: No, KGH is not congruent to GKH. 81. ANS: x 2 + (y + 1) 2 = 25 4
46 82. ANS: Statements Reasons 1. AB BC and DC BC 1. Given 2. B and C are right angles 2. Definition of sperpendicular lines 3. B C 3. All right angles are congruent 4. AD bisects BC at E 4. Given 5. BE EC 5. Definition of segment bisector 6. AEB and DEC are vertical 6. Definition of vertical angles angles 7. ABE DCE 7. ASA 8. AB DC 8. CPCTC 83. ANS: x = 9 y = ANS: h = ANS: TE = ANS: DF = 30 OA = ANS: AB = 2 5
47 88. ANS: mab = ANS: ( x + 3) 2 + Ê Ë Á y 2ˆ 2 = ANS: ANS: r 22.4 cm 92. ANS: EB ANS: x = ANS: CD = ANS: V = 2016 m ANS: Center: (3, 4) radius: 10 6
48 97. ANS: m QPT = ANS: CE = ANS: P = ANS: x = ANS: ( x 5) 2 + Ê Ë Á y + 4ˆ 2 = ANS: m BAD = ANS: 3 cans of paint are needed ANS: m C = 30 7
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