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Geometry Final Exam Review
Name______________________________________________Date____________Period______
1. Find the length and midpoint of
___
QT given the coordinates: Q(−7, −4),

T(6, 10).
2. ∆ABC is an isosceles triangle with the
m<B = m<A. Identify the vertex, legs,
base, and base angles of the isosceles
triangle.
3. What type of angles are <3 and <4,
pictured below:
12. Find all of the numbered angles for the
rhombus:
13. Find the area of the trapezoid:
14. All segments shown in the figure below
4. Triangle NPR is isosceles, with vertex
5.
6.
7.
8.
angle P. PN is four times a number, NR
is two times the number, and PR is five
more than three times the number. Find
the perimeter of ∆NPR.
Find the sum of the interior angles of a
polygon with 11 sides.
An animal shelter has only dogs and
cats. Out of a total of 400 animals, 230
are cats. What is the ratio of dogs to
cats in simplest form?
A circle has a radius of 34 inches. What
are the circumference and area of the
circle to the nearest tenth?
Use trigonometry to find x for the
triangle:
are tangent to the circle. Suppose that
segment PQ is drawn to form ∆BPQ. If
the m<A = 85°, the m<D = 110°, and
the m<C = 95°, then what are the
measures of <B, <BPQ, and <BQP?
15. For parallelogram ABCD, find the Area,
and all of the angle measures (use
trigonometry).
16. Find the lateral area, surface area, and
9. Is ∆TSO congruent to ∆EOS? If so,
volume of the cylinder below in terms of
π.
state the congruence theorem or
postulate that proves them congruent.
17. Find the lateral area, surface area, and
volume of the cone below to the nearest
tenth.
10. A 4-foot-tall model of a building in
Charlotte casts a 1-foot shadow at the
same time the building casts a 55-foot
shadow. How tall is the building to the
nearest foot?
11. A 12-foot ramp leans on the back of a
moving truck. The angle of depression
of the ramp is 20O. How high off of the
ground is the back of the moving truck?
18. Find the volume of the triangular prism,
shown below, to the nearest centimeter.
Geometry Final Exam Review
Name______________________________________________Date____________Period______
27. Find the length of segment XY for the
19. For the diagram below, the m<PQM =
trapezoid:
4x – 6 and the m<NQM = 3x + 32.
What is the m<KQP?
28. Triangle ABC has vertices A(15,-9), B(20. Is the following statement always true,
sometimes true, or never true?
If one angle of a triangle measures 90
degrees, then the other two angles of the
triangle each measure 45 degrees.
3,0), and C(12,6). Find the coordinates
of the vertices for a dilation centered at
the origin with scale factor of -½.
29. Find the circumference and area of the
following circle in terms of π.
21. Find the value of x for which a || b.
30. Find x for the picture below:
22. Find x, y, and z for the right triangle
shown below:
23. Find the missing sides of the right
31. A parallelogram has a base of 20 inches,
sides 13 inches, and a height of 8 inches.
Find the area and perimeter of the
parallelogram.
32. What type of solid is shown below?
Identify its bases.
triangle:
33. What is the surface area to the nearest
24. What are the coordinates of the
intersection of the diagonals of
parallelogram ABCD with vertices:
A(1,-2), B(0,6), C(4,8), and D(5,0)?
25. Find x for the rectangle shown below:
26. Describe, under what circumstance:
a. A parallelogram will be a
rectangle
b. A rectangle is a square.
c. A rhombus is a square.
tenth of a right cylinder with a height of
25 feet and a base diameter of 12 feet?
34. A sphere has a radius of 5.2 inches.
Find its volume to the nearest tenth.
35. If <ABC and <ABD form a linear pair,
what is the m<ABC if the m<ABD is
72º?
36. What is the converse, inverse, and
contrapositive of the following
statement?
If x2 = 49, then x = 7.
37. What is the slope of a line parallel to
line RS and perpendicular to RS, given:
R(5, 2) and S(−2, 4).
38. What is sinX, cosX, and tanX for:
Geometry Final Exam Review
Name______________________________________________Date____________Period______
39. Angle B in triangle ABC measures 90º.
49. A square has a diagonal length of 12
If sides BA and BC each measure 18
meters, then find the measures of <A,
<C, and side AC.
40. What is the measure of an exterior angle
of a regular pentagon?
41. The Bank of America Corporate Center,
in Uptown Charlotte, is 871 feet tall.
What is the angle of elevation to the top
of the building from a point on the
ground 354 feet from the building’s
base?
42. Find x for the triangle below:
centimeters. What is its Area?
50. Find the surface area of a square
pyramid with a height of 11 centimeters
and a base edge measuring 20
centimeters.
51. The volume of a rectangular prism is
240 cubic inches, the length is 8 inches,
and the width is 3 inches. What is the
height?
52. Find the area of a circle with a diameter
of 22 meters in terms of π.
53. The segment measuring 8 units is
tangent to circle P, shown below. Find
the value of x.
43. Ray BD bisects <ABC, so that the
m<DBA = 3x – 9 and the m<DBC =
6x – 39. What is the m<ABC?
44. What plane is parallel to Plane ABC in
the figure:
54. Which algebraic property is shown here:
If x = y and y = z, then x = z
55. For the town map shown below, list
each pair of locations whose location
exhibits an alternate exterior angle
relationship:
45. What other piece of information would
you need to know in order to prove that
∆PAL is congruent to ∆RLA by SAS?
56. Refer to the picture above. The museum
46. Find x and y for the diagram shown
below:
47. A 15-foot flagpole casts a 3-foot
shadow. A near by mailbox casts a 1foot shadow. How tall is the mailbox to
the nearest foot?
48. Find x in the figure below:
sits on the corner of two streets that
form an 80º angle with one another.
Your friend says that the post office also
sits on the corner of two streets that
form an 80º angle with one another. Is
he correct? Explain.
57. Y is the midpoint of segment XZ. If
XY = 2x – 5 and YZ = x + 10, then what
is the measure of XY?
58. Find the perimeter of a regular hexagon
if one of its sides measures 3x and
another measures 9x – 54.
59. If QR = ST, and ST = 12, then QR = 12.
What property justifies this statement?
Geometry Final Exam Review
Name______________________________________________Date____________Period______
60. If a dog barks, then it is hungry. What
is the converse of this statement?
61. What is the inverse of the statement
above?
62. A regular nonagon has a perimeter of 72
feet. What is the length of one side of
the nonagon?
63. Find the distance between A(2,3) and
B(-1,4) to the nearest hundredth.
64. B is between A and C. If AB = 3x,
BC = 7x – 12, and AC = 18, find the
length of BC.
65. Find x for the picture below:
(x – 2)2 + (y + 3)2 = 64
73. Find the area of a regular hexagon with
a side length of 10 inches in radical
form.
74. A bag contains 10 blue marbles, 6 red
marbles, and 11 green marbles. What is
the probability of selecting a blue or red
marble from the bag?
75. The equation of a parabola is x = y2 – 2y
+ 4. What is the equation for the axis of
symmetry of the parabola?
76. For the diagram below, the m<A = 35º,
the m<CED = 65º, AB = 5, AE = 6, and
CD = 3. Find the scale factor between
the two triangles, the m<C, and the
length of segment DE.
66. Find x for the picture below:
77. Are the triangles shown below similar to
67. Find x and y for the picture below:
one another? If so, state the similarity
postulate or theorem that proves them
similar.
68. Find x and y for the picture below:
78. What algebraic property justifies the
statement: m<A = m<A.
79. The measures of two angles of a triangle
69. Find the exact values (non-decimal) of x
and y for the right triangle:
70. Find the values of x and y for the right
triangle:
are 50º and 25º. Classify the triangle as
right, obtuse, or acute.
80. Find the measure of each angle of the
following polygon:
81. Find the measure of each numbered
angle for the following parallelogram:
71. A square has a perimeter of 20
centimeters. What is the length of a
diagonal of the square in radical form?
72. What is the center and radius of a circle
given by the equation:
82. Find x and y for the figure below:
Geometry Final Exam Review
Name______________________________________________Date____________Period______
Solutions:
1. Midpoint: (-0.5,3); Distance: √365 or
19.1
2. Vertex: <C; Legs: CA & CB; Base: AB;
and Base Angles: <A & <B
3. Same-Side Interior Angles
4. 50
5. 1620O
6. 17:23
7. C = 213.6 inches; A = 3631.7 inches2
8. x = 49.5O
9. Yes, by AAS
10. 220 feet
11. 4.1 feet
12. m<1 = 50O, m<2 = 90O,
m<3 = m<4 = 40O
13. 15 inches2
14. m<B = 70O, m<BPQ = m<BQP = 55O
15. Area = 128 inces2, m<A = m<C = 53.1O,
m<B = m<D = 126.9O
16. LA = 30π, SA = 48π, V = 45π
17. LA = 55.0, SA = 83.2, V = 47.1
18. V = 4 cm2
19. 8o
20. Sometimes True
21. 54
22. x = √70 = 8.4; y = √21 = 4.6;
z = √30 = 5.5
23. The other leg is 4 cm and the
hypotenuse is 4√2 cm.
24. (2.5,3)
25. 7
26. Part a: If the diagonals are congruent or
if it has one right angle
Part b: If its sides are congruent, if the
diagonals are perpendicular, if the
diagonals bisect opposite angles
Part c: If the diagonals are congruent, if
it has one right angle
27. 12
28. A(-7.5,4.5); B(1.5,0); C(-6,-3)
29. C = 15π, A = 56.25π
30. 14.8
31. A = 160 inches2, P = 66 inches
32. Triangular Prism, Bases ∆ABC & ∆DEF
33. 1168.7 feet2
34. 589.0 inches3
35. 108o
36. Converse: If x = 7, then x2 = 49
Inverse: If x2 ≠ 49, then x ≠ 7
Contrapositive: If x ≠ 7, then x2 ≠ 49
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
Parallel:-2/7; Perpendicular: 7/2
sinx = 12/13; cosX = 5/13; tanX = 5/12
m<A = m<C = 45o; AC = 18√2
72o
67.9o
11.2
42o
Plane DEF
You would need to know that segment
PA is congruent to segment RL.
x = 17 and y = 35
5 feet
x=7
72 cm2
994.6 cm2
10 inches
121π
x = 10
Transitive property
Museum & High School AND Playing
Fields & Library
No. Although the locations are alternate
interior to one another, there is no
indication that the streets are parallel.
25
162
Transitive property
If a dog is hungry, then it barks.
If a dog doesn’t bark, then it is not
hungry.
8
3.16
BC = 9
11.5
5.6
x = 112.5o; y = 67.5o
x = 193o and y = 60.5o
x = 15√3 and y = 30
x & y = 24
5√2
C(2,-3) and r = 8
150√3
16/27
y=1
SF: 5/3; m<C = 80o; DE = 36
Yes, by SSS Similarity
Reflexive Property
Obtuse, the last angle would be 105o
100o and 105o are the missing angles
<1 = <2 = 45o, <3 = 80o, <4 = 55o
x = 130; y = 108
Geometry Final Exam Review
Name______________________________________________Date____________Period______