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
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Slope, Quadrilateral, Parallelogram, opposite sides

Click to edit the document details