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Geometry 300
Midterm Review
Name_________________________
Date_____________________
1. In the figure shown, HG  IJ , IH  5, FJ  24, and JG  4. Find FI .
H
I
F
J
G
2. In ACE, BD  AE , AE  56, DE  12, CD  x, and BD  14. Find CE.
C
B
D
A
3. The supplement of an angle is ten more than double the complement. Define the
variables and find the angle, complement and supplement.
4. The ratio of the measures of the angles of a quadrilateral is 3:7:11:15. What is the
measure of each angle in the quadrilateral?
5. The measures of the sides of an isosceles trapezoid are in the ratio of 5.5 : 4 : 5.5 : 10.
If the perimeter of the trapezoid is 300 feet, then what is the length of the median of the
trapezoid?
E
Geometry 300
Midterm Review
Name_________________________
Date_____________________
6. Give 4 different ways to name the angle to the right.
Define the following terms:
7. right angle
8. straight angle
9. obtuse angle
10. acute angle
11. linear pair
12. Find the complement and supplement of 52 .
13. Find the complement and supplement of 103 .
14. In the diagram at the right, name 3 collinear points.
15. In the diagram at the right, name 3 noncollinear points.
16. Given square ABCD with the diagonals intersecting at point E. Find mDBA .
Geometry 300
Midterm Review
Name_________________________
Date_____________________
17. In rectangle OPQR, the diagonals intersect at point S. If OS = 12, then find OQ +
PR.
18. The bases of a trapezoid are (9x + 3) and (13x + 1). If the median is (12x - 4), find
the value of x.
19. WV is a base of isosceles trapezoid TUVW. If mW   3x  6  and
mV  5x  28 , then find the value of x.
20. In parallelogram ABCD, mA   4 x  8  and mD  13x  18  . Find mC .
21. In rectangle JKLM, the diagonals intersect at point N. If JN  x 2  2 x and
KM  4x  24 , then find the value(s) of x that make this problem work and find the
length(s) of JL .
Geometry 300
Midterm Review
Name_________________________
Date_____________________
In problems 22-27, determine whether the triangles are congruent (use SSS, SAS, ASA or
AAS). If they are congruent, write the postulate that proves they are congruent. If they
are not congruent, write “NC.”
22.
23.
24.
25.
26.
27.
28. In rectangle ABCD, the diagonals AC and BD intersect in point E. If AE = 2x + 3
and BE = 12 – x, find BD.
A.
B.
C.
D.
3
9
18
None of the above.
Geometry 300
Midterm Review
Name_________________________
Date_____________________
29. In rectangle ABCD, the diagonals AC and BD intersect in point E. If
mBAC  3x  5 and mACD  40  2 x , find mAED .
A.
B.
C.
D.
52
7
26
None of the above.
30. In square ABCD the diagonals intersect at E, mDAC  y and mBAC  3x . Find
x.
A.
B.
C.
D.
15
30
60
None of the above.
For problems 31 and 32, list ALL the names that apply to a quadrilateral with the
given vertices. Then circle the name that BEST applies. Show mathematical proof
of your answer (this means slopes and distances).
31. E(0, -3), F(-3, 0), G(0, 3), H(3, 0)
32. P(1, 3), Q(-3, -1), R(-2, -8), S(8, 2)
Geometry 300
Midterm Review
Name_________________________
Date_____________________
33. Given parallelogram PQRS with  P = 7x and Q = 8x + 30, find the measures of
 R and S .
Use parallelogram ABCD and the given information to find each value.
34. AC = 5x – 12 and AT = 14. Find x.
35. BC = 4x + 7 and AD = 8x – 5. Find x.
36. m<BCD = 3x + 14 and m<ADC = x + 10. Find m<ADC.
Geometry 300
Midterm Review
Name_________________________
Date_____________________
37. If quadrilateral BLUE is a rectangle, find the value of x.
b) EB = x2 - 10, UL = x + 20
a) LP = 7x - 3, UB = 78
38. ABC is equilateral, AB =
1
x  8 and BC  3x  3 . Find x, AC , and find the
2
perimeter of the triangle.
39. Find the value of x, mA and mB.
A
B
4x + 20o
40o
C
40. Given DEF with mD  (7b  1) o , mE  (2b  1) o and mF  (b  8) o . Find b,
mE and classify the triangle by its angles.
Geometry 300
Midterm Review
Name_________________________
Date_____________________
41. Find y and mJHK .
G
H
(14y – 14)o
(6y)o
(7y – 3)o
K
J
42. Determine the value of x in the diagram.
77o
xo
154o
43. In the diagram, a // b . Find the m1.
70o
44. In the diagram, a // b . Find the m2
a
15o
35o
b
2
1
45. In the diagram, a // b and c // d . Find the m3 .
3
a
40o
b
c
d
95o
a
b
Geometry 300
Midterm Review
Name_________________________
Date_____________________
46. In LMN , the measure of the largest angle is 32 less than 3 times the smallest angle.
The measure of the middle angle is 8 more than half the measure of the largest angle.
Draw and label a diagram. Use your knowledge of Geometry and Algebra to determine
the measure of the middle angle.
3 o
5
y , mS  y o ,
2
2
mSQR  ( x 2  5x  66) o and mPQS  100 o . Find the values of x, y and the measures
of S and  R .
47. In the diagram, QRS is acute, mR 
R
S
Q
P
48. In the diagram below, a || b , m6  115 and m2  70 . Find m3 .
Geometry 300
Midterm Review
Name_________________________
Date_____________________
49. Using the diagram below (which is not necessarily drawn to scale), if
m3  66  x 2 and m 2  (12 x  21) , find the value(s) of x, then find all reasonable
values for m8 .
50. Find the values of x and y.
51. Find the values of x, y and z.
52. Find the values of x, y and z.
Geometry 300
Midterm Review
Name_________________________
Date_____________________
53. M and N are vertical angles. Are M and N right angles if
mM  4 x  14 and mN  6 x  24 ?
Use the diagram at right. If the stated information is true, name the lines which would be
parallel. If no lines would be parallel, write “none.”
54. 13  8
______________
56.  6   2
______________
57.  2   7
______________
58. 8   9
______________
59.  7  15
______________
60. 1   9
______________
61. 10  11
______________
62.  4  10  180 ______________
63. Given point A(-20, 13) and point B(-24, 60), do the following:
a) find the length AB to the nearest hundredth,
b) find the coordinates of the midpoint of AB using the MIDPOINT FORMULA.
Geometry 300
Midterm Review
Name_________________________
Date_____________________
64. An obtuse angle has a measure of (15x + 15). What is the range of possible values
for x?
65. The sum of three times an angle and four times its complement exceeds twice its
supplement by 15. Find the measure of the angle, its complement and its supplement.
66. Determine the possible values of x. Use the value(s) of x that make sense for this
problem to find the measures of the four angles.
67. Find the value of x, y and mFCD if
mF  10 x  8 y  14
mFCB  4 x  5 y  2
mFBC  3x  5 y  36
Geometry 300
Midterm Review
Name_________________________
Date_____________________
True or False:
68. _____ An angle can be named by its vertex.
69. _____ A line contains two planes.
70. _____ If A, B, and C are distinct point on a line, then AB + BC = AC.
71. _____ A midpoint must be positive.
72. _____ If line k lies in plane M, then the intersection of the line k and plane M is a
point.
Always – Sometimes – Never (write A, S or N)
73. _____ If a ray divides an angle into two acute angles, then that ray bisects the angle.
74. _____ If two angles are adjacent and congruent, then they are vertical angles.
75. _____ If two intersecting lines form congruent adjacent angles, then the lines are
perpendicular.
76. _____ If two angles are supplementary, then they are a linear pair.
77. ____ If two angles are supplementary and congruent, then they are right angles.
78. EF has endpoint E(3, 7) and midpoint M(-4, 6). Find the coordinates of
endpoint B.
79. In the figure at right CX bisects AB at X and CD bisects XB at Y. Given the
following conditions, find the value of x and the measure of the indicated
segment.
a. AX = 2x + 11, XB = 4x – 5; find AB
b. AB = x + 3, AX = 3x – 1; find XB
Geometry 300
Midterm Review
Name_________________________
Date_____________________
80. In the figure at the right, TE bisects  GTM and TO bisects
 ETM. mOTM = 7x – 5 and mGTE = 15x-17. Find mGTO.
81. Using the diagram at the right, name a segment that is skew to AB .
82. Using the diagram at the right, name a segment that is parallel to AB .
83. Using the diagram at the right, name a plane parallel to plane FBC.
84. Are the following points collinear? Use algebra to prove your conclusion.
A(-5, 9), B(-1, 1), C(1, -4)
85. In the diagram, r t. Find m3.