Exam view geotrig final s1 2011

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. If mCDA  66, then
mBCD  ? . 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, mKLO  68 and
mMLO  61. Find KJM. The diagram is not to
scale.
a. 119
b. 61
c. 129
d. 68

Name: ________________________ ID: A
2
6. Find AM in the parallelogram if PN =9 and AO = 4.
The diagram is not to scale.
a. 8
b. 4
c. 9
d. 4.5
7. Find the values of a and b.The diagram is not to
scale.
a. a  144, b  67
b. a  144, b  36
c. a  113, b  67
d. a  113, b  36
8. Find m1 and m3 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 of x. The diagram is not to scale.
a. 32
b. 50
c. 64
d. 80

Name: ________________________ ID: A
3
10. Points B, D, and F are midpoints of the sides of
ACE. EC = 30 and DF = 23. Find AC. The
diagram is not to scale.
a. 30
b. 11.5
c. 60
d. 46
11. The length of DE 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 of TSR. Find the
value of x. 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?
II. on the triangle
a. I only
b. III only
c. I or III only
d. I, II, or II

Name: ________________________ ID: A
4
16. In ABC, G is the centroid and BE = 9. Find BG
and GE.
a. BG = 2
1
4
, GE = 6
3
4
b. BG  3, GE  6
c. BG  6, GE  3
d. BG = 4
1
2
, GE = 4
1
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

Name: ________________________ ID: A
5
19. Find the length of AB, given that DB is a median of
the triangle and AC = 26.
a. 13
b. 26
c. 52
d. not enough information
20. Where can the medians of a triangle intersect?
II. on 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?
II. on 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 points A, B, and C?
a.
b.
c.
d.

Name: ________________________ ID: A
6
23. Name the smallest angle of ABC. 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
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 cm
c. 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 and x < 28
c. x > 10 and x < 18
d. x  10 and x  18
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. If BCDE is 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

Name: ________________________ ID: A
7
30. The two triangles are congruent as suggested by their appearance. Find the value of c. 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  DAC
b. CBA  CDA
c. AC  BD
d. AC BD
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 only
d. 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

Name: ________________________ ID: A
8
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

Name: ________________________ ID: A
9
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. AAS
d. none of these
39. Use the information in the figure. Find mD.
a. 32°
b. 122°
c. 64°
d. 58°
40. Given ABC  PQR, mB  3v  4, and
mQ  8v  6, find mB and mQ.
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

Name: ________________________ ID: A
10
42. Line r is parallel to line t. Find m5. The diagram
is not to scale.
a. 45
b. 35
c. 135
d. 145
two parallel lines, then ____ angles are
supplementary.
a. acute
b. alternate interior
c. same-side interior
d. corresponding
44. Find mQ. The diagram is not to scale.
a. 60
b. 120
c. 110
d. 70
45. m1  6x and m3  120. Find the value of x for p
to be parallel to q. The diagram is not to scale.
a. 114
b. 126
c. 120
d. 20
46. Find the value of k. The diagram is not to scale.
a. 17
b. 73
c. 118
d. 107
a. 33
b. 162
c. 147
d. 75

Name: ________________________ ID: A
11
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  2
180
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)180
n
d. 180n
53. Find mA. 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 of
the 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.

Name: ________________________ ID: A
12
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 line M P.
c. Yes, they lie on the line NP.
d. Yes, they lie on the line MO.
57. Name the line and plane shown in the diagram.
a. RS

and plane RSU c. RS

and plane UR
b. line R and plane RSU d. SR

and plane UT
58. Name the ray in the figure.
a. BA

b. AB

c. BA d. AB

59. Find AC.
a. 14 b. 15 c. 12 d. 4

Name: ________________________ ID: A
13
60. If T is the midpoint of SU, find the values of x 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. If mEOF  26 and mFOG  38, then what is
the measure of EOG? 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. DOC
d. 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.

Name: ________________________ ID: A
14
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.
(Figures are not drawn to scale.)
65. mO  111
a. 291
b. 69
c. 55.5
d. 222
66. mP  12
a. 78
b. 39
c. 102
d. 24
Find the value of x. 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 of BAC. (The figure is not
drawn to scale.)
a. 57
b. 28.5
c. 33
d. 114

Name: ________________________ ID: A
15
Short Answer
69. DF bisects EDG. Find the value of x. The
70. Find the values of x and y. The diagram is not to
scale.
71. Find the values of x, y, and z. The diagram is not to
scale.
72. mA  9x  7, mB  7x  9, and mC  28  2x.
List the sides of ABC in order from shortest to
longest.
73. Q is equidistant from the sides of TSR. Find
mRST. The diagram is not to scale.
74. Find the value of x.
75. Use the information given in the diagram. Tell why
AC  AC and BCA  DAC.

Name: ________________________ ID: A
16
77. Find the values of the variables and the lengths of
the sides of this kite.
78. Find the values of x and y.
79. FG  OP, RS  OQ, FG = 40, RS = 37, OP = 19 80.

Name: ________________________ ID: A
17
81. JK, KL, and LJ are all tangent to O (not drawn to
scale). JA = 9, AL = 10, and
CK = 14. Find the perimeter of JKL.
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 mBAC. (The figure is not drawn to scale.)
84. MO

bisects LMN, mLMN  5x  23,
mLMO  x  32. Find mNMO. The diagram is
not to scale.
85. If EF  2x  12, FG  3x  15, and EG  23, find
the values of x, 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.
mDFG = x  5, and mJKL = x  9. Find the
measure of each angle.

Name: ________________________ ID: A
18
89. 1 and 2 are supplementary angles.
m1  x  39, and m2  x  61. Find the measure
of each angle.
90. Find the value of the variable if m Ä l,
m1 = 2x  44 and m5 = 5x  38. The diagram is
not to scale.
91. Find the coordinates of the midpoint of the segment
whose endpoints are H(8, 2) and K(6, 10).
92. DF

bisects EDG. Find FG. The diagram is not to
scale.

ID: A
1
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

ID: A
2
41. C
42. C
43. C
44. A
45. D
46. B
47. A
48. D
49. C
50. C
51. D
52. B
53. D
54. D
55. B
56. A
57. A
58. 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°

ID: A
3
83. 57
84. 61
85. x = 10, EF = 8, FG = 15
86. 78 in.
87. 225 in.2
88. DFG = 52, JKL = 38
89. 1  40, 2  140
90. 2
91. (7, 6)
92. 14

Name: ________________________________ Per: _________ Teacher: ___________________ Date: __________
ID: B
1
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. If mCDA  57, then
mBCD  ? . 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, mKLO  63 and
mMLO  66. Find KJM. The diagram is not to
scale.
a. 129
b. 66
c. 63
d. 119

Name: ________________________ ID: B
2
6. Find AM in the parallelogram if PN =14 and AO =
3. The diagram is not to scale.
a. 7
b. 6
c. 14
d. 3
7. Find the values of a and b.The diagram is not to
scale.
a. a  130, b  50
b. a  108, b  72
c. a  108, b  50
d. a  130, b  72
8. Find m1 and m3 in the kite. The diagram is not
to scale.
a. 24, 66
b. 66, 66
c. 66, 24
d. 24, 24
a. 25
b. 42
c. 60
d. 50

Name: ________________________ ID: B
3
10. Points B, D, and F are midpoints of the sides of
ACE. EC = 39 and DF = 24. Find AC. The
a. 78
b. 12
c. 48
d. 39
11. The length of DE 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 of TSR. Find the
value of x. The diagram is not to scale.
a. 12
b. 11.6
c. 25
d. 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?
II. on 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?
II. on the triangle
a. I only
b. III only
c. I, II, or II
d. I or III only

Name: ________________________ ID: B
4
16. In ABC, G is the centroid and BE = 21. Find BG
and GE.
a. BG = 5
1
4
, GE = 15
3
4
b. BG = 10
1
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

Name: ________________________ ID: B
5
19. Find the length of AB, given that DB is a median of
the triangle and AC = 22.
a. 22
b. 44
c. 11
d. not enough information
20. Where can the medians of a triangle intersect?
II. on 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?
II. on 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 points A, B, and C?
a.
b.
c.
d.

Name: ________________________ ID: B
6
23. Name the smallest angle of ABC. 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
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 cm
c. 19 cm, 5 cm, 7 cm
d. 8 cm, 25 cm, 10 cm
Which inequalities describe the values that possible
lengths for the third side?
a. x > 8 and x < 12
b. x > 4 and x < 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. If BCDE is 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

Name: ________________________ ID: B
7
30. The two triangles are congruent as suggested by their appearance. Find the value of b. 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. AC  BD
c. CBA  CDA
d. AC BD
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 SAS
d. 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

Name: ________________________ ID: B
8
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

Name: ________________________ ID: B
9
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 you
immediately conclude ABD  CBD.
a. AAS
b. SAS
c. ASA
d. none of these
39. Use the information in the figure. Find mD.
a. 62°
b. 31°
c. 59°
d. 121°
40. Given ABC  PQR, mB  2v  3, and
mQ  6v  5, find mB and mQ.
a. 17
b. 20
c. 7
d. 8
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

Name: ________________________ ID: B
10
42. Line r is parallel to line t. Find m5. The diagram
is not to scale.
a. 33
b. 133
c. 147
d. 23
two parallel lines, then ____ angles are
supplementary.
a. alternate interior
b. acute
c. corresponding
d. same-side interior
44. Find mQ. The diagram is not to scale.
a. 85
b. 105
c. 75
d. 109
45. m1  5x and m3  115. Find the value of x for p
to be parallel to q. The diagram is not to scale.
a. 23
b. 110
c. 115
d. 120
46. Find the value of k. The diagram is not to scale.
a. 114
b. 43
c. 91
d. 89
a. 145
b. 51
c. 106
d. 74

Name: ________________________ ID: B
11
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)180
b.
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)180
n
d. (n – 2)180
53. Find mA. 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 of
the 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.

Name: ________________________ ID: B
12
56. Are P, Q, and R 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 plane M NP c. line M and plane M NP
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. Find AD.
a. 14 b. 8 c. 2 d. 16

Name: ________________________ ID: B
13
60. If T is the midpoint of SU, find the values of x 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. If mEOF  35 and mFOG  27, then what is
the measure of EOG? 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. DOE
d. 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.

Name: ________________________ ID: B
14
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.
(Figures are not drawn to scale.)
65. mO  101
a. 281
b. 202
c. 79
d. 50.5
66. mP  11
a. 39.5
b. 22
c. 101
d. 79
67.
a. 100
b. 50
c. 20
d. 40
68. Find the measure of BAC. (The figure is not
drawn to scale.)
a. 69
b. 138
c. 34.5
d. 21

Name: ________________________ ID: B
15
Short Answer
69. DF bisects EDG. Find the value of x. The
70. Find the values of x and y. The diagram is not to
scale.
71. Find the values of x, y, and z. The diagram is not to
scale.
72. mA  8x  2, mB  2x  8, and mC  94  4x.
List the sides of ABC in order from shortest to
longest.
73. Q is equidistant from the sides of TSR. Find
mRST. The diagram is not to scale.
74. Find the value of x.
75. Use the information given in the diagram. Tell why
PS  QR and QRP  SPR.

Name: ________________________ ID: B
16
77. Find the values of the variables and the lengths of
the sides of this kite.
78. Find the values of x and y.
79. FG  OP, RS  OQ, FG = 37, RS = 38, OP = 17 80.

Name: ________________________ ID: B
17
81. JK, KL, and LJ are all tangent to O (not drawn to
scale). JA = 13, AL = 11, and
CK = 15. Find the perimeter of JKL.
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 mBAC. (The figure is not drawn to scale.)
84. MO

bisects LMN, mLMN  5x  27,
mLMO  x  33. Find mNMO. The diagram is
not to scale.
85. If EF  2x  16, FG  3x  19, and EG  20, find
the values of x, 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.
mDFG = x  1, and mJKL = x  3. Find the
measure of each angle.

Name: ________________________ ID: B
18
89. 1 and 2 are supplementary angles.
m1  x  25, and m2  x  77. Find the measure
of each angle.
90. Find the value of the variable if m Ä l,
m1 = 6x  40 and m5 = 8x  18. The diagram is
not to scale.
91. Find the coordinates of the midpoint of the segment
whose endpoints are H(9, 15) and K(3, 9).
92. DF

bisects EDG. Find FG. The diagram is not to
scale.

ID: B
1
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

ID: B
2
41. B
42. C
43. D
44. C
45. A
46. C
47. D
48. B
49. A
50. A
51. D
52. B
53. A
54. C
55. C
56. A
57. A
58. 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°

ID: B
3
83. 48
84. 64
85. x = 11, EF = 6, FG = 14
86. 90 in.
87. 576 in.2
88. DFG = 47, JKL = 43
89. 1  39, 2  141
90. 11
91. (6, 12)
92. 6

Exam view geotrig final s1 2011

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