Name _______________________________________________ Date ___________________ Period ____
Geometry: Final Exam Study Guide
For problems 1-3, find each numbered
angle and give a reason for each answer.
1.
35
4
2
3
1
55
1
55
2
40
45
7. Given XYZ with points X(-3, 1),
Y(1, 4) and Z(5, 2). The triangle is
reflected across the x-axis to form
XYZ. Find the point Z.
8. Given XYZ with points X(0, 2),
Y(0, 5) and Z(-2, 4). The triangle is
rotated 90 counterclockwise around the
origin to form XYZ. Find the
point Z.
2.
4
6. Given ABC with points A(-1, 5),
B(-2, -3) and C(2, 3). The triangle is
translated to form ABC where A
is the point (4, 2). Find the point B
3
13. Find x and y in the figure given
M and N are midpoints.
y
M 78
N
x
31
24
14. Find x and y in the figure given
M and N are midpoints.
65
M
2x + 8
14
y
N
40
9. Given XYZ with points X(4, 0), Y(8,
0) and Z(5, 3). The triangle is rotated 180 
counterclockwise around the origin to
15. Find x in the rectangle
form XYZ. Find the point Z.
3.
85
a.
b.
c.
3
35
1
x
10. Can the following set of three sides
form a triangle? Yes or no.
2
20
14, 20, 34
4, 19, 4
11, 5, 8
16. Find x in the rhombus.
4
4. Name the transformation shown in the
figure below:
x
11. Find the maximum and minimum
values for the third side of a triangle
with two sides given
a.
b.
25
60 and 62
14 and 20
17. Find x and y in the parallelogram.
12. List the three angles of the triangle
in order from smallest to largest.
20
Y
5. Given ABC with points A(1, 5),
B(6, 3) and C(8, 7). The triangle is
reflected across the y-axis to form
ABC. Find the point B.
60
7
x
10
y
18
X
21
Z
Name _______________________________________________ Date ___________________ Period ____
Geometry: Final Exam Study Guide
For problems 18-31, if the two triangles
shown are congruent, give a reason (SSS,
SAS, ASA, AAS, or HL) why they are
congruent and write a correct congruence
statement. If there is not enough
information to say the triangles are
congruent, write “not congruent”.
18.
A
O
22.
.27.
D
K
G
E
M
J
F
B
C
E
23.
N
L
28.
B
E
D
A
F
19.
H
G
P
C
D
24.
29.
B
Q
20.
T
R
A
X
C
Y
Z
D
X
Y
V
W
X
Y
25.
30.
A
B
W
Z
V
21.
E
D
Z
W
31.
F
26.
G
X
Y
H
H
Z
I
W
K
J
Name _______________________________________________ Date ___________________ Period ____
Geometry: Final Exam Study Guide
32. Find the sum of the measures of the
exterior angles of a 20-gon.
For problems 41-53, find x in each figure.
41.
48.
55
33. Find the measure of one exterior angle
of a regular 15-gon
20
3x - 10
34. The measure of one interior angle of a
regular polygon is 120. Find the
number of sides of the polygon.
35. The measure of one exterior angle of a
regular polygon is 40. Find the
number of sides of the polygon.
33
x
49.
42.
9x
x+5
36. Find x in the diagram below:
x + 15






4x
50
50
50.
x
75
50
70
80
2x + 10
40
60
43.
70
x + 30
51.
37. Find the sum of the measures of the
interior angles of a hexagon.
38. Find the measure of one interior angle
of a regular 15-gon
x + 50
4x + 40
44.
25






4x
100
52.
39. The sum of the measures of the interior
angles of a polygon is 3240. Find the
number of sides of the polygon.
x + 40
5x
5x + 20
40. Find x in each diagram below.
a.
x
45.
53.
100
30
25
2x + 50
x
b.
120
x
130
x
100
80
4x - 30
Name _______________________________________________ Date ___________________ Period ____
Geometry: Final Exam Study Guide
For problems 54-, find x in each figure.
54.
61. For each pair of points, find the
midpoint and length of the segment
connecting the points.
a.
66.
12
9
(-3, 1) and (4, 4)
6
3x + 22
20
5x - 2
b.
55.
(-1, 2) and (-7, -6)
67.
1 and 2 are complementary.
m1 = 3x + 10
m2 = 2x
Find x.
7
22
For problems 62-63, use the Pythagorean
Theorem to find the length of x.
62.
9
56.
12
x + 20
4x - 10
4
x
For problems 68-69, find the area and
perimeter of each figure.
68.
15
57. m AOC = 130
63.
B
8
12
7
A
16
45
2x - 5
O
x
C
58. 1 and 2 are supplementary
m1 = 3x
m2 = x + 20
Find x.
For problems 64-68, find the area of each
figure.
c.
If x = 12, then x2 = 144.
65.
If a number is odd, then it is
divisible by three.
If a figure is a square, then all of its
angles are right angles.
8
6
5
14
70. Find the area of the shaded region.
4
8
15
17
60. Write an indirect proof to show that a
triangle can have at most one obtuse
angle.
8
9
64.
59. Write the inverse, converse, and
contrapositive of the conditional
statement. Decide whether the
converse is true or false. If false,
provide a counterexample.
a.
b.
69.
29
35