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

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.