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Since opposite sides have the same slope,
B
w
C
w
i
D
w
E
w
and
B
w
E
w
i
C
w
D
w
. Therefore,
BCDE
is a parallelogram
by definition.
9.
Yes;
First use the Distance Formula to determine
whether the opposite sides are congruent.
AD
5
Ï
(
x
2
2
w
x
1
)
2
1
w
(
y
2
2
w
y
1
)
2
w
5
Ï
[
2
6
2
w
(
2
4)]
w
2
1
(3
w
2
0)
2
w
5
Ï
13
w
BC
5
Ï
(1
2
3
w
)
2
1
(4
w
2
1)
2
w
5
Ï
13
w
Since
AD
5
BC
,
A
w
D
w
>
B
w
C
w
.
Next, use the Slope Formula to determine
whether
A
w
D
w
i
B
w
C
w
.
slope of
A
w
D
w
5
}
y
x
2
2
2
2
y
x
1
1
}
5
}
2
6
3
2
2
(
0
2
4)
}
52
}
3
2
}
slope of
B
w
C
w
5
}
4
1
2
2
1
3
}
}
3
2
}
A
w
D
w
and
B
w
C
w
have the same slope, so they are
parallel. Since one pair of opposite sides is
congruent and parallel,
ABCD
is a parallelogram.
10.
No;
If the midpoints of the diagonals are the same,
the diagonals bisect each other. If the diagonals of
a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
Find the midpoints of
E
w
G
w
and
F
w
H
w
.
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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, Slope

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