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145
Chapter 5
14.
In
n
ABO
and
n
CBO
,
A
w
B
w
>
C
w
B
w
,
O
w
B
w
>
O
w
B
w
, and
m
/
CBO
,
m
/
ABO
.The SAS Inequality allows
us to conclude that
OC
,
OA
.
15.
In
n
ABC
,
A
w
B
w
>
C
w
B
w
so
n
ABC
is isosceles with
base angles of measure
}
1
2
}
[180
2
(40
1
60)] or 40.
m
/
AOB
5
¬
180
2
(
m
/
OAB
1
m
/
ABO
)
5
¬
180
2
(40
1
60)
5
¬
80
m
/
AOD
5
¬
180
2
m
/
AOB
5
¬
100
Therefore,
m
/
AOD
.
m
/
AOB
.
16.
By the SAS Inequality, 10
,
3
x
2
2.
10
¬
,
3
x
2
2
12
¬
,
3
x
4
¬
,
x
or
x
.
4
17.
The triangle on the left is equilateral, so all
angles have measure 60. Then by the SAS
inequality,
x
1
2
.
2
x
2
8.
x
1
2
¬
.
2
x
2
8
2
¬
.
x
2
8
10
¬
.
x
The measure of any side is always greater than 0.
2
x
2
8
¬
.
0
2
x
¬
.
8
x
¬
.
4
The two inequalities can be written as the
compound inequality 4
,
x
,
10.
18.
M
w
C
w
>
M
w
C
w
, so by the SSS Inequality
m
/
1
.
m
/
2.
5
x
1
20
¬
.
8
x
2
100
20
¬
.
3
x
2
100
120
¬
.
3
x
40
¬
.
x
The measure of any angle is always greater
than 0.
8
x
2
100
¬
.
0
8
x
¬
.
100
x
¬
.
12.5
The two inequalities can be written as the
compound inequality 12.5
,
x
,
40.
19.
/
RTV
>
/
TRV
, so
n
RVT
is isosceles and
R
w
V
w
>
T
w
V
w
.
S
w
V
w
>
S
w
V
w
and
RS
,
ST
, so by the SSS
Inequality,
m
/
RVS
,
m
/
SVT
.
15
1
5
x
¬
,
10
x
2
20
15
¬
,
5
x
2
20
35
¬
,
5
x
7
¬
,
x
The measure of
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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