255
Chapter 8
For (2,
2) and (0, 4),
RT
QS
.
slope of
SR
¬
1
1
(
(
1
1
)
)
¬
1
Suppose
T
is (0, 4).
slope of
QT
¬
0
4
(
2
2)
¬
1
So
SR
QT
.
So, (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
KM
and
JL
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:
AD
BC
AB
DC
Prove:
ABCD
is a
parallelogram.
Proof:
40. Given:
AE
EC
,
DE
EB
Prove:
ABCD
is a parallelogram.
Proof:
41. Given:
AB
DC
AB
DC
Prove:
ABCD
is a parallelogram.
Proof:
42.
This theorem is not true.
ABCD
is a
parallelogram with diagonal
BD
,
ABD
CBD
.
43. Given:
ABCDEF
is a regular hexagon.
Prove:
FDCA
is a parallelogram.
Proof:
44.
Sample answer: The roofs of some covered bridges
are parallelograms. The opposite sides are
congruent and parallel. Answers should include
the following.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Slope, Trigraph, Quadrilateral, Parallelogram

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