Pre-Calculus Homework Solutions 253 - 41 Given AB DC AB DC...

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.