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23. Given:
a
.
0,
b
.
0, and
a
.
b
Prove:
}
a
b
}
.
1
Proof:
Step 1
Assume that
}
a
b
}
±
1.
Step 2
Case 1
Case 2
}
a
b
}
¬
,
¬
1
}
a
b
}
¬
5
1
a
¬
,
¬
ba
¬
5
b
Step 3
The conclusion of both cases contradicts
the given fact
a
.
b
.
Thus,
}
a
b
}
.
1.
24. Given:
A
w
B
w
>
@
A
w
C
w
Prove:
/
1
>
@
/
2
Proof:
Step 1
Assume that
/
1
>
/
2.
Step 2
If
/
1
>
/
2, then the sides opposite the
angles are congruent.
Thus
A
w
B
w
>
A
w
C
w
.
Step 3
The conclusion contradicts the given
information. Thus
/
1
>
/
2 is false.
Therefore,
/
1
>
@
/
2.
25. Given:
n
ABC
and
n
ABD
are equilateral.
n
ACD
is not equilateral.
Prove:
n
BCD
is not equilateral.
Proof:
Step 1
Assume that
n
BCD
is an equilateral
triangle.
Step 2
If
n
BCD
is an equilateral triangle, then
B
w
C
w
>
C
w
D
w
>
D
w
B
w
.Since
n
ABC
and
n
ABD
are equilateral triangles,
A
w
C
w
>
A
w
B
w
>
B
w
C
w
and
A
w
D
w
>
A
w
B
w
>
D
w
B
w
.By the Transitive
Property,
A
w
C
w
>
A
w
D
w
>
C
w
D
w
. Therefore,
n
ACD
is an equilateral triangle.
Step 3
This conclusion contradicts the given
information. Thus, the assumption is false.
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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

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