examview - geotrig final s1 2011

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    Name: ________________________________ Per: _________ Teacher: ___________________ Date: __________

    ID: A

    1

    Geometry/Trigonometry Final S1

    Multiple Choice

    Identify the choice that best completes the statement or answers the question.

    1. Judging by appearance, classify the figure in as

    many ways as possible.

    a. rectangle, square, quadrilateral, parallelogram,

    rhombus

    b. rectangle, square, parallelogram

    c. rhombus, trapezoid, quadrilateral, square

    d. square, rectangle, quadrilateral

    2. Which statement is true?

    a. All quadrilaterals are rectangles.

    b. All quadrilaterals are squares.

    c. All rectangles are quadrilaterals.

    d. All quadrilaterals are parallelograms.

    3. ABCD is a parallelogram. IfmCDA 66, then

    mBCD ? . The diagram is not to scale.

    a. 66

    b. 124

    c. 114

    d. 132

    4. Find the values of the variables in the

    parallelogram. The diagram is not to scale.

    a. x 49,y 29,z 102

    b. x 29,y 49,z 131

    c. x 49,y 49,z 131

    d. x 29,y 49,z 102

    5. In the parallelogram, mKLO 68 and

    mMLO 61. Find KJM. The diagram is not to

    scale.

    a. 119

    b. 61

    c. 129

    d. 68

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    6. FindAMin the parallelogram ifPN=9 andAO = 4.

    The diagram is not to scale.

    a. 8

    b. 4

    c. 9

    d. 4.5

    7. Find the values ofa and b.The diagram is not to

    scale.

    a. a 144,b 67

    b. a 144,b 36c. a 113,b 67

    d. a 113,b 36

    8. Find m1 and m3 in the kite. The diagram is not

    to scale.

    a. 51, 51

    b. 39, 39

    c. 39, 51

    d. 51, 39

    9. Find the value ofx. The diagram is not to scale.

    a. 32

    b. 50

    c. 64

    d. 80

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    10. PointsB,D, and Fare midpoints of the sides of

    ACE.EC= 30 andDF= 23. FindAC. The

    diagram is not to scale.

    a. 30

    b. 11.5

    c. 60d. 46

    11. The length ofDE is shown. What other length can

    you determine for this diagram?

    a. EF= 12

    b. DG = 12

    c. DF= 24

    d. No other length can be determined.

    12. Q is equidistant from the sides ofTSR. Find the

    value ofx. The diagram is not to scale.

    a. 27

    b. 3

    c. 15

    d. 30

    13. Where is the center of the largest circle that you

    could draw inside a given triangle?

    a. the point of concurrency of the altitudes of the

    triangle

    b. the point of concurrency of the perpendicular

    bisectors of the sides of the triangle

    c. the point of concurrency of the bisectors of the

    angles of the triangle

    d. the point of concurrency of the medians of the

    triangle

    14. Where can the perpendicular bisectors of the sides

    of a right triangle intersect?

    I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I only

    b. II only

    c. I or II only

    d. I, II, or II

    15. Where can the bisectors of the angles of an obtuse

    triangle intersect?I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I only

    b. III only

    c. I or III only

    d. I, II, or II

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    16. In ABC,G is the centroid andBE= 9. FindBG

    and GE.

    a. BG = 21

    4, GE= 6

    3

    4

    b. BG 3,GE 6

    c. BG 6,GE 3

    d. BG = 41

    2

    , GE= 41

    2

    17. Name a median for ABC.

    a. AD

    b. CE

    c. AF

    d. BD

    18. Name the point of concurrency of the angle bisectors.

    a. A b. B c. C d. not shown

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    19. Find the length ofAB, given that DB is a median of

    the triangle andAC= 26.

    a. 13

    b. 26

    c. 52

    d. not enough information

    20. Where can the medians of a triangle intersect?

    I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I only

    b. III only

    c. I or III only

    d. I, II, or II

    21. Where can the lines containing the altitudes of an

    obtuse triangle intersect?

    I. inside the triangleII. on the triangle

    III. outside the triangle

    a. I only

    b. I or II only

    c. III only

    d. I, II, or II

    22. Which diagram shows a point P an equal distance

    from pointsA,B, and C?

    a.

    b.

    c.

    d.

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    23. Name the smallest angle ofABC. The diagram is

    not to scale.

    a. A

    b. C

    c. Two angles are the same size and smaller than

    the third.

    d. B

    24. List the sides in order from shortest to longest. The

    diagram is not to scale.

    a. LK,LJ,JK

    b. LJ,LK,JK

    c. LJ,JK,LK

    d. LK,JK,LJ

    25. Which three lengths could be the lengths of the

    sides of a triangle?

    a. 12 cm, 5 cm, 17 cm

    b. 10 cm, 15 cm, 24 cmc. 9 cm, 22 cm, 11 cm

    d. 21 cm, 7 cm, 6 cm

    26. Two sides of a triangle have lengths 10 and 18.

    Which inequalities describe the values that possible

    lengths for the third side?

    a. x 8 and x 28

    b. x > 8 andx < 28

    c. x > 10 andx < 18

    d. x 10 and x 18

    27. Two sides of a triangle have lengths 10 and 15.

    What must be true about the length of the third

    side?

    a. less than 25

    b. less than 10

    c. less than 15

    d. less than 5

    28. IfBCDEis congruent to OPQR, then DE is

    congruent to ? .

    a. PQ

    b. OR

    c. OP

    d. QR

    29. ABC ?

    a. PMN

    b. NPM

    c. NMP

    d. MNP

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    30. The two triangles are congruent as suggested by their appearance. Find the value ofc. The diagrams are not to

    scale.

    a. 4 b. 5 c. 3 d. 38

    31. What other information do you need in order to

    prove the triangles congruent using the SAS

    Congruence Postulate?

    a. BAC DACb. CBA CDA

    c. ACBD

    d. ACBD

    32. State whether ABC and AED are congruent.

    Justify your answer.

    a. yes, by either SSS or SAS

    b. yes, by SSS only

    c. yes, by SAS onlyd. No; there is not enough information to

    conclude that the triangles are congruent.

    33. Name the angle included by the sides PN and NM.

    a. N

    b. P

    c. M

    d. none of these

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    34. In each pair of triangles, parts are congruent as

    marked. Which pair of triangles is congruent by

    ASA?

    a.

    b.

    c.

    d.

    35. From the information in the diagram, can you prove

    FDG FDB? Explain.

    a. yes, by ASA

    b. yes, by AAA

    c. yes, by SAS

    d. no

    36. Can you use the ASA Postulate, the AAS Theorem,

    or both to prove the triangles congruent?

    a. either ASA or AAS

    b. ASA only

    c. AAS only

    d. neither

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    37. Based on the given information, what can you

    conclude, and why?

    Given:H L,HJ JL

    a. HIJ LKJ by ASA

    b. HIJ JLK by SAS

    c. HIJ JLK by ASA

    d. HIJ LKJ by SAS

    38. Name the theorem or postulate that lets you

    immediately conclude ABD CBD.

    a. SAS

    b. ASA

    c. AASd. none of these

    39. Use the information in the figure. Find mD.

    a. 32

    b. 122

    c. 64

    d. 58

    40. Given ABC PQR,mB 3v 4, and

    mQ 8v 6, find mB and mQ.

    a. 22

    b. 11

    c. 10

    d. 25

    41. Complete the statement. If a transversal intersects

    two parallel lines, then ____.

    a. corresponding angles are supplementary

    b. same-side interior angles are complementary

    c. alternate interior angles are congruent

    d. none of these

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    42. Line ris parallel to line t. Find m5. The diagram

    is not to scale.

    a. 45

    b. 35

    c. 135

    d. 145

    43. Complete the statement. If a transversal intersects

    two parallel lines, then ____ angles are

    supplementary.

    a. acute

    b. alternate interior

    c. same-side interior

    d. corresponding

    44. Find mQ. The diagram is not to scale.

    a. 60

    b. 120

    c. 110

    d. 70

    45. m1 6x and m3 120. Find the value ofx forp

    to be parallel to q. The diagram is not to scale.

    a. 114

    b. 126

    c. 120

    d. 20

    46. Find the value ofk. The diagram is not to scale.

    a. 17

    b. 73

    c. 118d. 107

    47. Find the value ofx. The diagram is not to scale.

    a. 33

    b. 162

    c. 147

    d. 75

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    48. How many sides does a regular polygon have if

    each exterior angle measures 20?

    a. 17 sides

    b. 20 sides

    c. 21 sides

    d. 18 sides

    49. Find the missing angle measures. The diagram is

    not to scale.

    a. x = 124,y = 125

    b. x = 56,y = 114

    c. x = 114,y = 56

    d. x = 56,y = 124

    50. The sum of the measures of two exterior angles of a

    triangle is 255. What is the measure of the third

    exterior angle?

    a. 75

    b. 115

    c. 105

    d. 95

    51. The Polygon Angle-Sum Theorem states: The sum

    of the measures of the angles of an n-gon is ____.

    a. n

    2180

    b. (n 1)180

    c.180

    n 1

    d. (n 2)180

    52. Complete this statement. The sum of the measures

    of the exterior angles of an n-gon, one at each

    vertex, is ____.

    a. (n 2)180

    b. 360

    c. (n 2)180n

    d. 180n

    53. Find mA. The diagram is not to scale.

    a. 107

    b. 117

    c. 63

    d. 73

    54. Based on the pattern, what are the next two terms ofthe sequence?

    9, 15, 21, 27, . . .

    a. 33, 972

    b. 39, 45

    c. 162, 972

    d. 33, 39

    55. Based on the pattern, what is the next figure in the

    sequence?

    a.

    b.

    c.

    d.

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    56. Are O,N, and P collinear? If so, name the line on which they lie.

    a. No, the three points are not collinear.

    b. Yes, they lie on the lineM P.

    c. Yes, they lie on the lineNP.

    d. Yes, they lie on the lineMO.

    57. Name the line and plane shown in the diagram.

    a. RS

    and planeRSU c. RS

    and plane UR

    b. lineR and planeRSU d. SR

    and plane UT

    58. Name the ray in the figure.

    a. BA

    b. AB

    c. BA d. AB

    59. FindAC.

    a. 14 b. 15 c. 12 d. 4

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    60. IfTis the midpoint ofSU, find the values ofx and

    ST. The diagram is not to scale.

    a. x = 5, ST= 45

    b. x = 5, ST= 60

    c. x = 10, ST= 60

    d. x = 10, ST= 45

    61. IfmEOF 26 and mFOG 38, then what is

    the measure ofEOG? The diagram is not to scale.

    a. 64

    b. 12

    c. 52

    d. 76

    62. Name an angle supplementary to EOD.

    a. BOC

    b. BOE

    c. DOCd. BOA

    63. How are the two angles related?

    a. vertical

    b. supplementary

    c. complementary

    d. adjacent

    64. Which angle is a right angle?

    a.

    b.

    c.

    d.

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    Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value ofx.

    (Figures are not drawn to scale.)

    65. mO 111

    a. 291

    b. 69

    c. 55.5

    d. 222

    66. mP 12

    a. 78

    b. 39

    c. 102

    d. 24

    Find the value ofx. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

    67.

    a. 13

    b. 26

    c. 77

    d. 38.5

    68. Find the measure ofBAC. (The figure is not

    drawn to scale.)

    a. 57

    b. 28.5

    c. 33

    d. 114

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    Short Answer

    69. DF bisects EDG. Find the value ofx. The

    diagram is not to scale.

    70. Find the values ofx andy. The diagram is not to

    scale.

    71. Find the values ofx,y, andz. The diagram is not to

    scale.

    72. mA 9x 7,mB 7x 9, and mC 28 2x.

    List the sides ofABCin order from shortest to

    longest.

    73. Q is equidistant from the sides ofTSR. Find

    mRST. The diagram is not to scale.

    74. Find the value ofx.

    75. Use the information given in the diagram. Tell why

    AC AC and BCA DAC.

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    76. Find the value ofx. The diagram is not to scale.

    77. Find the values of the variables and the lengths of

    the sides of this kite.

    78. Find the values ofx andy.

    Find the value ofx. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

    79. FG OP, RS OQ, FG = 40,RS = 37, OP = 19 80.

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    81. JK, KL, and LJ are all tangent to O (not drawn to

    scale). JA = 9,AL = 10, and

    CK= 14. Find the perimeter ofJKL.

    82. What is the measure of a base angle of an isosceles

    triangle if the vertex angle measures 38 and the

    two congruent sides each measure 21 units?

    83. Find mBAC. (The figure is not drawn to scale.)

    84. MO

    bisects LMN, mLMN 5x 23,

    mLMO x 32. Find mNMO. The diagram is

    not to scale.

    85. IfEF 2x 12, FG 3x 15, andEG 23, find

    the values ofx,EF, and FG. The drawing is not to

    scale.

    86. Find the circumference of the circle in terms of.

    87. Find the area of the circle in terms of.

    88. DFG and JKL are complementary angles.

    mDFG = x 5, and mJKL = x 9. Find the

    measure of each angle.

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    89. 1 and 2 are supplementary angles.

    m1 x 39, and m2 x 61. Find the measure

    of each angle.

    90. Find the value of the variable ifm l,m1 = 2x 44 and m5 = 5x 38. The diagram is

    not to scale.

    91. Find the coordinates of the midpoint of the segment

    whose endpoints areH(8, 2) and K(6, 10).

    92. DF

    bisects EDG. Find FG. The diagram is not to

    scale.

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    ID: A

    1

    Geometry/Trigonometry Final S1

    Answer Section

    MULTIPLE CHOICE

    1. A

    2. C

    3. C

    4. D

    5. C

    6. B

    7. A

    8. C

    9. C

    10. D

    11. A

    12. B

    13. C

    14. B

    15. A

    16. B

    17. D

    18. C

    19. A

    20. A

    21. C

    22. A

    23. D

    24. C

    25. B

    26. B

    27. A

    28. D

    29. D

    30. C

    31. C

    32. A

    33. A

    34. B

    35. A

    36. A

    37. A

    38. A

    39. A

    40. C

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    ID: A

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    41. C

    42. C

    43. C

    44. A

    45. D

    46. B47. A

    48. D

    49. C

    50. C

    51. D

    52. B

    53. D

    54. D

    55. B

    56. A

    57. A58. A

    59. C

    60. A

    61. A

    62. C

    63. B

    64. C

    65. B

    66. A

    67. C

    68. B

    SHORT ANSWER

    69. 6

    70. x = 77,y = 57

    71. x 86, y 67, z 94

    72. AB;AC;BC

    73. 25

    74. 4

    75. Reflexive Property, Given

    76. x 23

    77. x = 9,y = 13; 11, 20

    78. x 90, y 43

    79. 20.5

    80. 13.5

    81. 66

    82. 71

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    ID: A

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    83. 57

    84. 61

    85. x =10,EF= 8, FG = 15

    86. 78in.

    87. 225in.2

    88. DFG = 52, JKL = 3889. 1 40, 2 140

    90. 2

    91. (7, 6)

    92. 14

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    Name: ________________________________ Per: _________ Teacher: ___________________ Date: __________

    ID: B

    1

    Geometry/Trigonometry Final S1

    Multiple Choice

    Identify the choice that best completes the statement or answers the question.

    1. Judging by appearance, classify the figure in as

    many ways as possible.

    a. square, rectangle, quadrilateral

    b. rhombus, trapezoid, quadrilateral, square

    c. rectangle, square, parallelogram

    d. rectangle, square, quadrilateral, parallelogram,

    rhombus

    2. Which statement is true?

    a. All quadrilaterals are squares.

    b. All rectangles are squares.

    c. All squares are quadrilaterals.

    d. All quadrilaterals are parallelograms.

    3. ABCD is a parallelogram. IfmCDA 57, then

    mBCD ? . The diagram is not to scale.

    a. 123

    b. 133

    c. 57

    d. 114

    4. Find the values of the variables in the

    parallelogram. The diagram is not to scale.

    a. x 57,y 21,z 102

    b. x 21,y 57,z 123

    c. x 21,y 57,z 102

    d. x 57,y 57,z 123

    5. In the parallelogram, mKLO 63 and

    mMLO 66. Find KJM. The diagram is not to

    scale.

    a. 129

    b. 66

    c. 63

    d. 119

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    6. FindAMin the parallelogram ifPN=14 andAO =

    3. The diagram is not to scale.

    a. 7

    b. 6

    c. 14

    d. 3

    7. Find the values ofa and b.The diagram is not to

    scale.

    a. a 130,b 50

    b. a 108,b 72c. a 108,b 50

    d. a 130,b 72

    8. Find m1 and m3 in the kite. The diagram is not

    to scale.

    a. 24, 66

    b. 66, 66

    c. 66, 24

    d. 24, 24

    9. Find the value ofx. The diagram is not to scale.

    a. 25

    b. 42

    c. 60

    d. 50

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    10. PointsB,D, and Fare midpoints of the sides of

    ACE.EC= 39 andDF= 24. FindAC. The

    diagram is not to scale.

    a. 78

    b. 12

    c. 48d. 39

    11. The length ofDE is shown. What other length can

    you determine for this diagram?

    a. EF= 14

    b. DG = 14

    c. DF= 28

    d. No other length can be determined.

    12. Q is equidistant from the sides ofTSR. Find the

    value ofx. The diagram is not to scale.

    a. 12

    b. 11.6

    c. 25d. 5

    13. Where is the center of the largest circle that you

    could draw inside a given triangle?

    a. the point of concurrency of the perpendicular

    bisectors of the sides of the triangle

    b. the point of concurrency of the bisectors of the

    angles of the triangle

    c. the point of concurrency of the medians of the

    triangle

    d. the point of concurrency of the altitudes of the

    triangle

    14. Where can the perpendicular bisectors of the sides

    of a right triangle intersect?

    I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I or II only

    b. I, II, or II

    c. I only

    d. II only

    15. Where can the bisectors of the angles of an obtuse

    triangle intersect?I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I only

    b. III only

    c. I, II, or II

    d. I or III only

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    16. In ABC,G is the centroid andBE= 21. FindBG

    and GE.

    a. BG = 51

    4, GE= 15

    3

    4

    b. BG = 101

    2, GE= 10

    1

    2

    c. BG 7,GE 14

    d. BG 14,GE

    7

    17. Name a median for ABC.

    a. AD

    b. AF

    c. BD

    d. CE

    18. Name the point of concurrency of the angle bisectors.

    a. A b. C c. B d. not shown

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    19. Find the length ofAB, given that DB is a median of

    the triangle andAC= 22.

    a. 22

    b. 44

    c. 11

    d. not enough information

    20. Where can the medians of a triangle intersect?

    I. inside the triangle

    II. on the triangle

    III. outside the triangle

    a. I or III only

    b. I, II, or II

    c. I only

    d. III only

    21. Where can the lines containing the altitudes of an

    obtuse triangle intersect?

    I. inside the triangleII. on the triangle

    III. outside the triangle

    a. I only

    b. I or II only

    c. III only

    d. I, II, or II

    22. Which diagram shows a point P an equal distance

    from pointsA,B, and C?

    a.

    b.

    c.

    d.

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    23. Name the smallest angle ofABC. The diagram is

    not to scale.

    a. A

    b. Two angles are the same size and smaller than

    the third.

    c. C

    d. B

    24. List the sides in order from shortest to longest. The

    diagram is not to scale.

    a. LJ,LK,JK

    b. JK,LK,LJ

    c. JK,LJ,LK

    d. LJ,JK,LK

    25. Which three lengths could be the lengths of the

    sides of a triangle?

    a. 9 cm, 15 cm, 22 cm

    b. 13 cm, 5 cm, 18 cmc. 19 cm, 5 cm, 7 cm

    d. 8 cm, 25 cm, 10 cm

    26. Two sides of a triangle have lengths 8 and 12.

    Which inequalities describe the values that possible

    lengths for the third side?

    a. x > 8 andx < 12

    b. x > 4 andx < 20

    c. x 8 and x 12

    d. x 4 and x 20

    27. Two sides of a triangle have lengths 7 and 14. What

    must be true about the length of the third side?

    a. less than 14

    b. less than 21

    c. less than 7

    d. less than 7

    28. IfBCDEis congruent to OPQR, then CD is

    congruent to ? .

    a. OP

    b. PQ

    c. QR

    d. OR

    29. PNM ?

    a. ACB

    b. BCA

    c. CBA

    d. BAC

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    30. The two triangles are congruent as suggested by their appearance. Find the value ofb. The diagrams are not to

    scale.

    a. 5 b. 4 c. 37 d. 3

    31. What other information do you need in order to

    prove the triangles congruent using the SAS

    Congruence Postulate?

    a. BAC DAC

    b. ACBD

    c. CBA CDA

    d. ACBD

    32. State whether ABC and AED are congruent.

    Justify your answer.

    a. yes, by SSS only

    b. yes, by SAS only

    c. yes, by either SSS or SASd. No; there is not enough information to

    conclude that the triangles are congruent.

    33. Name the angle included by the sides MP and PN.

    a. N

    b. P

    c. M

    d. none of these

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    34. In each pair of triangles, parts are congruent as

    marked. Which pair of triangles is congruent by

    ASA?

    a.

    b.

    c.

    d.

    35. From the information in the diagram, can you prove

    FDG FDB? Explain.

    a. yes, by AAA

    b. yes, by ASA

    c. yes, by SAS

    d. no

    36. Can you use the ASA Postulate, the AAS Theorem,

    or both to prove the triangles congruent?

    a. either ASA or AAS

    b. ASA only

    c. AAS only

    d. neither

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    37. Based on the given information, what can you

    conclude, and why?

    Given:M Q,MO OQ

    a. MNO QPO by ASA

    b. MNO OQP by SAS

    c. MNO OQP by ASA

    d. MNO QPO by SAS

    38. Name the theorem or postulate that lets youimmediately conclude ABD CBD.

    a. AAS

    b. SAS

    c. ASAd. none of these

    39. Use the information in the figure. Find mD.

    a. 62

    b. 31

    c. 59

    d. 121

    40. Given ABC PQR,mB 2v 3, and

    mQ 6v 5, find mB and mQ.

    a. 17

    b. 20

    c. 7

    d. 8

    41. Complete the statement. If a transversal intersects

    two parallel lines, then ____.

    a. same-side interior angles are complementary

    b. alternate interior angles are congruent

    c. corresponding angles are supplementary

    d. none of these

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    42. Line ris parallel to line t. Find m5. The diagram

    is not to scale.

    a. 33

    b. 133

    c. 147

    d. 23

    43. Complete the statement. If a transversal intersects

    two parallel lines, then ____ angles are

    supplementary.

    a. alternate interior

    b. acute

    c. corresponding

    d. same-side interior

    44. Find mQ. The diagram is not to scale.

    a. 85

    b. 105

    c. 75

    d. 109

    45. m1 5x and m3 115. Find the value ofx forp

    to be parallel to q. The diagram is not to scale.

    a. 23

    b. 110

    c. 115

    d. 120

    46. Find the value ofk. The diagram is not to scale.

    a. 114

    b. 43

    c. 91d. 89

    47. Find the value ofx. The diagram is not to scale.

    a. 145

    b. 51

    c. 106

    d. 74

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    48. How many sides does a regular polygon have if

    each exterior angle measures 20?

    a. 17 sides

    b. 18 sides

    c. 21 sides

    d. 20 sides

    49. Find the missing angle measures. The diagram is

    not to scale.

    a. x = 109,y = 68

    b. x = 119,y = 116

    c. x = 68,y = 109

    d. x = 68,y = 119

    50. The sum of the measures of two exterior angles of a

    triangle is 260. What is the measure of the third

    exterior angle?

    a. 100

    b. 90

    c. 110

    d. 80

    51. The Polygon Angle-Sum Theorem states: The sum

    of the measures of the angles of an n-gon is ____.

    a. (n

    1)180b.

    180

    n 1

    c.n 2

    180

    d. (n 2)180

    52. Complete this statement. The sum of the measures

    of the exterior angles of an n-gon, one at each

    vertex, is ____.

    a. 180n

    b. 360

    c. (n 2)180n

    d. (n 2)180

    53. Find mA. The diagram is not to scale.

    a. 73

    b. 63

    c. 117

    d. 107

    54. Based on the pattern, what are the next two terms ofthe sequence?

    7, 16, 25, 34, . . .

    a. 306, 2754

    b. 52, 61

    c. 43, 52

    d. 43, 2754

    55. Based on the pattern, what is the next figure in the

    sequence?

    a.

    b.

    c.

    d.

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    56. Are P, Q, andR collinear? If so, name the line on which they lie.

    a. Yes, they lie on the line PR.

    b. Yes, they lie on the line PS.

    c. No, the three points are not collinear.

    d. Yes, they lie on the line QS.

    57. Name the line and plane shown in the diagram.

    a. MN

    and planeMNP c. lineMand planeMNP

    b. MN

    and plane PM d. NM

    and plane PO

    58. Name the ray in the figure.

    a. QP

    b. PQ

    c. PQ

    d. QP

    59. FindAD.

    a. 14 b. 8 c. 2 d. 16

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    60. IfTis the midpoint ofSU, find the values ofx and

    ST. The diagram is not to scale.

    a. x = 7, ST= 42

    b. x = 12, ST= 56

    c. x = 12, ST= 42

    d. x = 7, ST= 56

    61. IfmEOF 35 and mFOG 27, then what is

    the measure ofEOG? The diagram is not to scale.

    a. 70

    b. 62

    c. 8

    d. 54

    62. Name an angle supplementary to COD.

    a. BOD

    b. COB

    c. DOEd. AOE

    63. How are the two angles related?

    a. vertical

    b. complementary

    c. adjacent

    d. supplementary

    64. Which angle is an acute angle?

    a.

    b.

    c.

    d.

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    Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value ofx.

    (Figures are not drawn to scale.)

    65. mO 101

    a. 281

    b. 202

    c. 79

    d. 50.5

    66. mP 11

    a. 39.5

    b. 22

    c. 101

    d. 79

    Find the value ofx. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

    67.

    a. 100

    b. 50

    c. 20

    d. 40

    68. Find the measure ofBAC. (The figure is not

    drawn to scale.)

    a. 69

    b. 138

    c. 34.5

    d. 21

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    Short Answer

    69. DF bisects EDG. Find the value ofx. The

    diagram is not to scale.

    70. Find the values ofx andy. The diagram is not to

    scale.

    71. Find the values ofx,y, andz. The diagram is not to

    scale.

    72. mA 8x 2,mB 2x 8, and mC 94 4x.

    List the sides ofABCin order from shortest to

    longest.

    73. Q is equidistant from the sides ofTSR. Find

    mRST. The diagram is not to scale.

    74. Find the value ofx.

    75. Use the information given in the diagram. Tell why

    PS QR and QRP SPR.

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    76. Find the value ofx. The diagram is not to scale.

    77. Find the values of the variables and the lengths of

    the sides of this kite.

    78. Find the values ofx andy.

    Find the value ofx. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

    79. FG OP, RS OQ, FG = 37,RS = 38, OP = 17 80.

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    81. JK, KL, and LJ are all tangent to O (not drawn to

    scale). JA = 13,AL = 11, and

    CK= 15. Find the perimeter ofJKL.

    82. What is the measure of a base angle of an isosceles

    triangle if the vertex angle measures 48 and the

    two congruent sides each measure 21 units?

    83. Find mBAC. (The figure is not drawn to scale.)

    84. MO

    bisects LMN, mLMN 5x 27,

    mLMO x 33. Find mNMO. The diagram is

    not to scale.

    85. IfEF 2x 16, FG 3x 19, andEG 20, find

    the values ofx,EF, and FG. The drawing is not to

    scale.

    86. Find the circumference of the circle in terms of.

    87. Find the area of the circle in terms of.

    88. DFG and JKL are complementary angles.

    mDFG = x 1, and mJKL = x 3. Find the

    measure of each angle.

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    89. 1 and 2 are supplementary angles.

    m1 x 25, and m2 x 77. Find the measure

    of each angle.

    90. Find the value of the variable ifm l,m1 = 6x 40 and m5 = 8x 18. The diagram is

    not to scale.

    91. Find the coordinates of the midpoint of the segment

    whose endpoints areH(9, 15) and K(3, 9).

    92. DF

    bisects EDG. Find FG. The diagram is not to

    scale.

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    ID: B

    1

    Geometry/Trigonometry Final S1

    Answer Section

    MULTIPLE CHOICE

    1. D

    2. C

    3. A

    4. C

    5. A

    6. D

    7. D

    8. A

    9. D

    10. C

    11. A

    12. D

    13. B

    14. D

    15. A

    16. C

    17. C

    18. B

    19. C

    20. C

    21. C

    22. A

    23. C

    24. B

    25. A

    26. B

    27. B

    28. B

    29. C

    30. B

    31. B

    32. C

    33. B

    34. C

    35. B

    36. A

    37. A

    38. A

    39. B

    40. C

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    ID: B

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    41. B

    42. C

    43. D

    44. C

    45. A

    46. C47. D

    48. B

    49. A

    50. A

    51. D

    52. B

    53. A

    54. C

    55. C

    56. A

    57. A58. A

    59. A

    60. A

    61. B

    62. C

    63. D

    64. A

    65. C

    66. D

    67. D

    68. C

    SHORT ANSWER

    69. 18

    70. x = 76,y = 46

    71. x 88, y 69, z 92

    72. AC;AB;BC

    73. 25

    74. 7

    75. Given, Given

    76. x 22

    77. x = 8,y = 15; 10, 19

    78. x 90, y 38

    79. 16.4

    80. 14.2

    81. 78

    82. 66

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    ID: B

    83. 48

    84. 64

    85. x =11,EF= 6, FG = 14

    86. 90in.

    87. 576in.2

    88. DFG = 47, JKL = 4389. 1 39, 2 141

    90. 11

    91. (6, 12)

    92. 6