Since opposite sides have the same slope,BwCw i DwEwand BwEw i CwDw. Therefore,BCDEis a parallelogramby definition.9.Yes;First use the Distance Formula to determinewhether the opposite sides are congruent.AD5Ï(x22wx1)21w(y22wy1)2w5Ï[26 2w(24)]w21(3w20)2w5Ï13wBC5Ï(123w)21(4w21)2w5Ï13wSince AD5BC,AwDw>BwCw.Next, use the Slope Formula to determinewhether AwDwi BwCw.slope of AwDw5}yx2222yx11}5}26322(024)}52}32}slope of BwCw5}412213}}32}AwDwand BwCwhave the same slope, so they areparallel. Since one pair of opposite sides iscongruent and parallel,ABCDis a parallelogram.10.No;If the midpoints of the diagonals are the same,the diagonals bisect each other. If the diagonals ofa quadrilateral bisect each other, then thequadrilateral is a parallelogram.Find the midpoints of EwGwand FwHw.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.