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Geometry
Chapter 5 Review
Segment
Perpendicular Bisectors
are drawn perpendicular to
the sides of the triangle
passing through the side’s
midpoint.
Angle Bisectors are rays
that cut the angle in half.
The points on the angle
bisector are equidistant to
the sides of the angle.
Medians are drawn from an
angle to the midpoint of
the opposite side of the
triangle
Name ____________________
Point of
Concurrency
Circumcenter
Incenter
Centroid
Location in
Triangle
Associated Properties
Acute: inside
The circumcenter is
Right: On
equidistant to the
Obtuse: Outside vertices.
Always inside
Always inside
The incenter is
equidistant to the 3
sides of the triangle
Centroid is located
two-thirds of the
length of the median
from the angle.
AB  23 AC ; BC  13 AC
“balance point” of the
triangle
Altitudes are drawn from
an angle so that they are
perpendicular to the line
that contains the opposite
side.
Always, sometimes or never?
1)
A midsegment of a triangle will ___________ be parallel to one side of the triangle.
2)
The perimeter of the triangle formed by the midsegments of a triangle is _______
one half of the original triangle’s perimeter.
3)
The medians of a triangle will __________ intersect outside of the triangle.
4)
The perpendicular bisectors of a triangle will _______ intersect outside the figure.
5)
An altitude of a triangle is ___________ perpendicular to a side of the triangle.
6)
An angle bisector of a triangle goes from a vertex to the opposite side and cuts the
side in half, __________.
7)
The shortest side of a triangle is _________ opposite the largest angle.
8)
3 inches, 6 inches and 9 inches could ________ be the sides of a triangle.
Define each term and draw a picture illustrating how it is located. Include all markings!
9)
circumcenter:
10)
What is its special property?
11)
incenter:
What is its special property?
centroid:
12)
midsegment:
What is its special property?
13)
Given:
A
FD is the perpendicular bisector of CE
CF is the angle bisector of ACE
Solve for the following values.
a) y = ______
h) mFCB = ______
b) CD = ______
i)
mCFB = ______
c) CE = ______
j)
mFBA = ______
d) x = ______
k) mBFA = ______
e) mFDE = ______
l)
f) mDCF = ______
m) mDFE = ______
F
B
112
44
3x - 5
C
2y - 7
D
E
y-3
mBAF = ______
g) mFED = ______
14)
EM and LM are  bisectors.
15) BD ,
CD , and AD are angle
bisectors.
A
B
5
y
F
E
7
G
L
x
10
M
y
B
z
9
A
D
x
6
E
K
x = ___________
Simplify the radical.
y = ___________
x = _____ y = _____ z = _____
C
16)
Point E is the centroid of
ABC . Find the indicated lengths:
DE  ________
CF  ________
EF  ________
BD  ________
CD  ________
Perimeter DEB  ________
EB  ________
Perimeter EFC  ________
A
G
4
14
10
C
16
E
D
F
12
B
17)
Determine whether or not each of the following sets of numbers can represent the
lengths of sides of a triangle. Write “yes” or “no” and show why.
a)
18)
b)
1, 1, 3
c)
6, 6, 7,
d)
12, 25, 13
Given two sides of a triangle, state the restrictions that apply to the 3rd side. Write
this as an inequality using x as the third side.
a)
19)
8, 17, 15
9, 10
b)
15, 25
c)
x=_______ y=________ z=________
1, 30,
20)
d)
7, 7
If the perimeter of COP is 60 cm,
what is the perimeter of BAD ? ____
O
z
x
y
40
60
C
21)
A
B
In RST, ST  RT and RT  RS.
a)
If one of the angles of the triangle
is obtuse, which angle must it be? _____
b)
If the measure of one of the angles
of the triangle is 60, which angle
must it be? _____
D
Sketch the triangle below
P
22)
List the sides of the triangle in order
from shortest to longest.
N
A
23)
List the angles of the triangle in
order from largest to smallest.
x-1
T
9
B
x+3
x
36
P
E
12
15
P
F
O
24)
List the 5 segments in the picture in
order from shortest to longest.
B
A
96
R
25)
60
List the 5 segments in order from
longest to shortest.
Q
81
40
55
T
D
72
80
26)
Suppose a triangle has angles which measure 50, 60,
and 70 and its sides have lengths of 3, 7, and 5. Draw a
sketch of the triangle, labeling all sides and angles.
27)
Complete each statement with  ,  , or =.
a) AB ____ DC
b)
mY _____ mW
A
B
40
45
25
A
M
N
20
Y
C
68
c) MO _____ MN
X
23
U
60
18
D
Z
W
58
O
P
28)
Solve for x in each problem. Use ,  , or = to set up the problem.
a)
b)
2x + 5
2x + 32
6
c)
54
50 50
9
9
68
66
6
29)
52
46
7x - 12
4x - 9
State whether each of the following inequality relationships is true or
false.
Given:
m5  m6
AB = BD
a)
m5  m1
T
F
b)
m3  mABC
T
F
c)
m2  m1
T
F
d)
BC  BA
T
F
C
6
2 D
1
3
4
B
30)
2x + 8
5
A
List the sides of STU in order from longest to shortest. mS  x  2 , mT  5x 1
and mU  2x  3