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8. Given:
n
ABC
is a right
triangle with
hypotenuse
B
w
C
w
.
M
is the midpoint
of
B
w
C
w
.
Prove:
M
is equidistant
from the vertices.
Proof:
The coordinates of
M
,the midpoint of
B
w
C
w
,
will be
1
}
2
2
c
}
,
}
2
2
b
}
2
5
(
c
,
b
).
The distance from
M
to each of the vertices can be
found using the Distance Formula.
MB
5
Ï
(
c
2
0
w
)
2
1
(
b
w
2
2
b
)
w
2
w
5
Ï
c
2
1
b
w
2
w
MC
5
Ï
(
c
2
2
w
c
)
2
1
(
w
b
2
0)
w
2
w
5
Ï
c
2
1
b
w
2
w
MA
5
Ï
(
c
2
0
w
)
2
1
(
b
w
2
0)
2
w
5
Ï
c
2
1
b
w
2
w
Thus,
MB
5
MC
5
MA
, and
M
is equidistant from
the vertices.
9. Given:
n
ABC
Prove:
n
ABC
is isosceles.
Proof:
Use the Distance Formula to find
AB
and
BC
.
AB
5
Ï
(2
2
0
w
)
2
1
(8
w
2
0)
2
w
5
Ï
4
1
64
w
or
Ï
68
w
BC
5
Ï
(4
2
2
w
)
2
1
(0
w
2
8)
2
w
5
Ï
4
1
64
w
or
Ï
68
w
Since
AB
5
BC
,
A
w
B
w
>
B
w
C
w
.Since the legs are
congruent,
n
ABC
is isosceles.
Pages 224–226
Practice and Apply
10.
• Use the origin as vertex
Q
of the triangle.
• Place the base of the triangle along the positive
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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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