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9/18/2015
Comparison Property of Inequality
If a  b  c and c  0, then a  b
b
c
a
Theorem 5-10
Corollary
The measure of
an exterior angle
of a triangle is
greater than the
measure of each
of the remote
interior angles
If
Then
m1  m2 and
m1  m3
1 is an exterior angle
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If
If two sides of a
triangle are not
congruent, then
the larger angle
lies opposite the
longer side.
Y
Z
X
If two angles of a
triangle are not
congruent, then
the longer side
lies opposite the
larger angle.
the diagram, list the sides in order from
smallest to largest.
mY  mZ
XZ  XY
Theorem 5-11
1
3
Then
If
Then
mA  mB
C
BC  AC
B
A
 In
Theorem
Diagram
The sum of
the lengths of
any two sides
of a triangle is
greater than
the third side.
Y
C
110°
B
AC , BC , BA
30°
mA  180  (30  110)
mA  40
A
X
XY  YZ  XZ
YZ  XZ  XY
XZ  XY  YZ
Z
1
9/18/2015
 Can
a triangle have side lengths of 4, 4, and
8? How about 4, 5, and 6?
44 8
45  6
46 5
88
96
10  5
No, a triangle
cannot be made
with side lengths
of 4, 4, and 8.
 P.

If two sides of a triangle are 8 and 14, what is
the range of possible lengths for the third side?
65  4
8  14  x
11  4
22  x
Yes, a triangle can be made with
side lengths of 4, 5, and 6. The sum
of the lengths of any two sides is
greater than the third.
8  x  14
x6
x  14  8
x  6
The length of a side of a triangle can never be negative so
we can eliminate that answer. So the range of values is
between 6 and 22.
6  x  22
328 #’s 6-12, 17, 20, 24-29, 37-39
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