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22. Given:
P
w
R
w
>
P
w
Q
w
,
SQ
.
SR
Prove:
m
/
1
,
m
/
2
Proof:
23. Given:
E
w
D
w
>
D
w
F
w
;
m
/
1
.
m
/
2;
D
is the midpoint
of
C
w
B
w
;
A
w
E
w
>
A
w
F
w
.
Prove:
AC
.
AB
Proof:
24. Given:
R
w
S
w
¬
>
U
w
W
w
S
w
T
w
¬
>
W
w
V
w
RT
¬
.
UV
Prove:
m
/
S
.
m
/
W
Indirect Proof:
Step 1
Assume
m
/
S
±
m
/
W
.
Step 2
If
m
/
S
±
m
/
W
,then either
m
/
S
,
m
/
W
or
m
/
S
5
m
/
W
.
Case 1:
If
m
/
S
,
m
/
W
,then
RT
,
UV
by the
SAS Inequality.
Case 2:
If
m
/
S
5
m
/
W
,then
n
RST
>
n
UWV
by
SAS, and
R
w
T
w
>
U
w
V
w
by CPCTC. Thus
RT
5
UV
.
Step 3
Both cases contradict the given
RT
.
UV
.
Therefore, the assumption must be false,
and the conclusion,
m
/
S
.
m
/
W
,must be
true.
25.
As the door is opened wider, the angle formed
increases and the distance from the end of the
door to the door frame increases.
26.
By the SAS Inequality Theorem, if the tree
started to lean, one of the angles of the triangle
formed by the tree, the ground, and the stake
would change, and the side opposite that angle
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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