247Chapter 843. Given:~MNPQ/Mis a right angle.Prove:/N,/Pand /Qare right anglesProof:By definition of a parallelogram,MwNwiQwPw.Since /Mis a right angle,MwQw ' MwNw.By thePerpendicular Transversal Theorem,MwQw ' QwPw./Qis a right angle, because perpendicular linesform a right angle./N>/Qand /M>/Pbecause opposite angles in a parallelogram arecongruent./Pand /Nare right angles, since allright angles are congruent.44. Given:ACDEis a parallelogram.Prove:EwCwbisects AwDw.AwDwbisects EwCw.Proof:It is given that ACDEis a parallelogram.Since opposite sides of a parallelogram arecongruent,EwAw>DwCw.By definition of aparallelogram,EwAwiDwCw./AEB>/DCBand/EAB>/CDBbecause alternate interior anglesare congruent.nEBA>nCBDby ASA.EwBw>BwCwand AwBw>BwDwby CPCTC. By the definition ofsegment bisector,EwCwbisects AwDwand AwDwbisectsEwCw.
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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.