255Chapter 8For (2,2) and (0, 4),RTQS.slope of SR¬11((11))¬1Suppose Tis (0, 4).slope of QT¬04(22)¬1So SRQT.So, (2,2), (4, 0), and (0, 4) are the possibilitiesfor the fourth vertex. Any of these values resultsin both pairs of opposite sides being parallel, andthus, the four points form a parallelogram.37.JKLMis a parallelogram because KMand JLarediagonals that bisect each other.38.If both pairs of opposite sides are parallel andcongruent, then the watchbox is a parallelogram.39. Given:ADBCABDCProve:ABCDis a parallelogram.Proof:40. Given:AEEC,DEEBProve:ABCDis a parallelogram.Proof:41. Given:ABDCABDCProve:ABCDis a parallelogram.Proof:42.This theorem is not true.ABCDis aparallelogram with diagonal BD,ABDCBD.43. Given:ABCDEFis a regular hexagon.Prove:FDCAis a parallelogram.Proof:44.Sample answer: The roofs of some covered bridgesare parallelograms. The opposite sides arecongruent and parallel. Answers should includethe following.
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