255
Chapter 8
For (2,
2
2) and (0, 4),
R
w
T
w
i
Q
w
S
w
.
slope of
S
w
R
w
5
¬
}
1
1
2
2
(
(
2
2
1
1
)
)
}
5
¬
1
Suppose
T
is (0, 4).
slope of
Q
w
T
w
5
¬
}
0
4
2
2
(
2
2
2)
}
5
¬
1
So
S
w
R
w
i
Q
w
T
w
.
So, (2,
2
2), (
2
4, 0), and (0, 4) are the possibilities
for the fourth vertex. Any of these values results
in both pairs of opposite sides being parallel, and
thus, the four points form a parallelogram.
37.
JKLM
is a parallelogram because
K
w
M
w
and
J
w
L
w
are
diagonals that bisect each other.
38.
If both pairs of opposite sides are parallel and
congruent, then the watchbox is a parallelogram.
39. Given:
A
w
D
w
>
B
w
C
w
A
w
B
w
>
D
w
C
w
Prove:
ABCD
is a
parallelogram.
Proof:
40. Given:
A
w
E
w
>
E
w
C
w
,
D
w
E
w
>
E
w
B
w
Prove:
ABCD
is a parallelogram.
Proof:
41. Given:
A
w
B
w
>
D
w
C
w
A
w
B
w
i
D
w
C
w
Prove:
ABCD
is a parallelogram.
Proof:
42.
This theorem is not true.
ABCD
is a
parallelogram with diagonal
B
w
D
w
,
/
ABD
±
/
CBD
.
43. Given:
ABCDEF
is a regular hexagon.
Prove:
FDCA
is a parallelogram.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Slope, Trigraph, Quadrilateral, Parallelogram

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