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Geometry Grade Level
Fall Semester 2014 Final Examination Review
Name_________________
Work each problem out. Completing the packet and showing work can get you up to five
bonus points on the final exam. You must show your work and you may use a calculator.
Round answers to the thousandths when needed.
For Questions 1 – 24, match the definition on the right with the vocabulary term on the left.
1.
2.
3.
4.
5.
6.
7.
____ inequality
____ray
____vertex
____corresponding angles
____obtuse
____congruent
____bisector
8. ____regular
9. ____equilateral triangle
10. ____isosceles triangle
11. ____SSS
12. ____parallel lines
13. ____ASA
14. ____acute
15. ____equidistant
16. ____midpoint
17. ____scalene
18. ____ 60
19. ____segment
20. ____180
21.
22.
23.
24.
____plane
____hypothesis
____slope
____polygon
a. the sum of the measures of all the angles in a triangle
b. a triangle in which no sides are congruent
c. the measure of each angle in an equilateral triangle
d. the state of being unequal in quantity or measure
e. a triangle with one angle greater than 90
f. coplanar lines which never intersect
g. a postulate relating two angles and the included side of
one triangle to the same for another triangle to show
congruence
h. being the same distance from two or more objects
i. a point equidistant from the two endpoints of a segment
j. a triangle in which all three sides are congruent
k. the ratio of the rise of a line or line segment to its run
l. a closed plane figure formed by three or more line
segments
m. having the same measure
n. a part of a line that starts at an endpoint and extends
forever in one direction
o. a postulate relating three sides of one triangle to three
sides of another to show congruence
p. the part of a conditional statement containing the word if
q. the part of a line containing two points and all the points
in between them
r. angles which lie on the same side of a transversal and on
the same sides of the two intersected lines
s. a triangle in which at least two sides are congruent
t. a line, ray, or line segment which cuts an angle or line
segment into equal parts
u. a flat surface that has no thickness and extends forever
v. a triangle with all angles less than 90
w. something both equilateral and equiangular
x. the common endpoint of two sides of a polygon
25. A large facility for relief distribution during disasters is located at coordinates (12, 17) . An
emergency occurs at (3, 12) . If the distance is measured in miles, estimate the number of miles it
is from the facility to the place where the emergency occurred.
_____
26. TC has endpoints T (8, 13) and C (302,10.28) . Find the midpoint of TC .
_____
27. The measure of an angle is 28.1 . Find the measure of its complement and its supplement.
complement_____
supplement_____
28. Which angles shown form a vertical pair?
a) G, Z
c) J , O
b) Z , P
d) G, P
Z
V
G
P
J
O
e) G, V
B
f) J , P
29. S is the midpoint of UA . US  14 x  5 units, and SA  20 x  37 units. Find the value of x
and the length of SA .
x _____
SA _____
MAT are complementary. Find the measures of both angles if
mGAT  (14 x  12) and mMAT  (6 x  28) .
mGAT ________ mMAT ________
30. GAT and
31. Identify the hypothesis and conclusion of the conditional statement If Paul brings his guitar
then we all sing.
32. Write the converse, the inverse, and the contrapositive of the conditional statement If she lives
in Lubbock then she is a Texan.
converse_________________________________________________________________________
inverse___________________________________________________________________________
contrapositive_____________________________________________________________________
33. Which value of x provides a counterexample to the conjecture shown to prove that the
conjecture is false?
Conjecture: For any positive number x ,
a) x  5
10
 x.
x
b) x  10
c) x  1
34. Write the following conditional statement as a biconditional.
If an angle is a straight angle then its measure is 180 .
________________________________________________________________________________
35. Help Mr. Juntti find the slope between the two points (16, 8) and (4,24) .
_____
36. Find the slope between the two points (2,18) and (2, 5) .
_____
37. Find the equation of the line with slope 10 passing through (3, 25) .
38. Coach Reed wanted to find out whether the lines given by y  2 
parallel, perpendicular, or neither. Help him decide.
__________
1
x and y  12  3x are
3
_____
39. Graph the line y  1 
2
( x  5) .
5
Use the illustration below for Questions 40 – 44. Lines U and L are parallel.
T
Y
K N
R A
Z C
U
L
F
40. Name a pair of vertical angles.
_____
41. Name a pair of same-side interior angles.
_____
42. Name the transversal.
_____
43. Name a pair of angles whose sum is 180 .
_____
44. If Z  (5x  12) and Y  (7 x  6) , find the measure of
Y .
45. Find x in the triangle shown.
_____
_____
11
(2 x  1)
(6 x  13)
46. Which property allows you to show that the two triangles below are congruent?
_____
47. A decoration on the side of the Hyatt Hotel in Baton Rouge is in the shape of an isosceles
triangle. If the two congruent angles in this triangle each measure 22.7 , what is the measure of the
third angle?
_____
48. While experimenting with background designs for the spring play, Mrs. Prudhomme planned a
triangular floor with all angles of equal measure. If she classified this triangle by its angle measure,
what type of triangle would it be?
_____
49. Mr. Clayton had to cordon off the perimeter of the silo construction site below. What is the
perimeter of the polygonal area shown?
_____
43 yds
54 yds
32
50. Given CAT  PIG . This means that IP  ________ .
51. A king built a small triangular playground for his daughters with each side twenty-seven meters
long. What is the measure of each angle in this playground?
_____
52. Find the measure of J .
_____
x
(3x)
144
53. Compare the lengths of ET and
BE .
29.1
30
m) ET  BE
J
n) ET  BE
T
o) ET  BE
B
E
54. Find the length of PN .
_____
140
180
P
N
180
140
220
55. Find the measure of LC given PH is the perpendicular bisector of LC .
_____
H
L
13
C
7
P
56. Write an equation in point-slope form for the perpendicular bisector of the segment with
endpoints (25,10) and (7,18) .
__________
57. Find UT .
U
_____
x  35
T
4 x  20
58. Mrs. Wolf’s large rectangular yard was 36 yards in length and 22 yards in width. Dogs
constantly ran from one corner diagonally to the other. Find the length of the diagonal of the yard.
_____
59. Find the length of the hypotenuse of the triangle.
_____
60
?
5
5 3
60. Which of the following would be a Pythagorean triple?
a) 24, 7, 25
b) 1, 2, 3
c) 1, 1,
2
d) 6, 8, 10
61. If NAM  90 , find the length of NA .
_____
A
43.8 in
M
N
45
62. A rectangular car lot has a length of 29 feet. The owner painted a stripe along the diagonal of
the lot going from corner to corner; the diagonal stripe is 39.5 feet long. Find the width of the lot.
_____
63. Determine if the conjecture is valid or not valid by using the Law of Detachment.
Given: If a student gets in a fight, then he is suspended. Raymond is suspended.
Conjecture: Raymond was in a fight.
_____
64. Determine if the conjecture is valid or not valid by using the Law of Syllogism.
Given: If Be’s ankle heals, she will join the girls track team. If she joins the girls track team, she will
run the 400  meter relay.
Conjecture: If Be’s ankle heals, she will run the 400  meter relay.
_____
65 and 66. Solve for x and y
X = ____________
y= ________________
67. Simplify the following to their simplest radical form.
a)
98
b)
30
5
c)
 64
d) 5.3 100
e)
x32
f) 2x x
7
68. Find the value of x and the lengths of the missing sides in the triangle shown. Do the side
lengths make a Pythagorean Triple?
_____________________
10
x
69. Given that
and NP .
x2
JKL  MNP , KL  21x  2 , NP  20 x , LJ  15 x , and PM  13x  4 . Find x
x ________ NP ________
70. Find the perpendicular bisector in point-slope form for the line segment between the points
(5,6) and (8,  4) .
________________________
71. Write the point-slope equation y  7 
3
( x  20) in slope-intercept form.
4
__________
72. Find the equation of the line containing (1, 11) and (4,  10) in slope-intercept form.
__________
Study the material in this review packet, along with Chapters 1 – 5 of the book, your
old notes, exams, and worksheets, and you will be prepared for the final examination!