梯形中位线的证明

BACEF三角形中位线定理三角形的中位线平行于第三边，并且等于它的一半即EF//BC，EF=½BCM梯形中位线定理梯形的中位线平行于两底，并且等于两底和的一半BCAEDF已知：梯形ABCD中，AD//BC，AE=EB，DF=FC求证：EF//BC，EF=½（BC+AD）证明：连结AF并延长，交BC的延长线于点M∵DF=FC，∠1=∠2，∠D=∠3，∴∆ADF≌∆MCF∴AF=MF，AD=CM又AE=EB∴EF是∆ABM的中位线∴EF//BC，EF=½BM∵BM=BC+CM=BC+AD∴EF=½（BC+AD）1231BACDEFGBACDEFNMBACDEFMNBACDEFGBACDEFGBACDEFNMBACDEFGBACDEFMNBACDEFGBACDEFGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFNMBACDEFBACDEFNMMNGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFMNBACDEFBACDEFNMMNBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMMNBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFGBACDEFBACDEFNMGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFBACDEFMNGBACDEFBACDEFBACDEFNMMNG知识巩固1梯形的上底长8，下底长10，则这个梯形的中位线长＿＿2梯形的上底长8，中位线长10，则下底长是＿＿3已知等腰梯形中位线长6cm，它的腰长5cm，则这个梯形的周长为＿＿＿cm4一个等腰梯形周长80，如果它的中位线与腰长相等，它的中位线长＿＿91222205梯形的中位线长9cm，一条对角线把中位线分成1:2两部分，则该梯形的下底长＿＿＿cm12例：一个等腰梯形的高是2，它的中位线长5，一个底角为45º，求这个梯形的上底，下底的长？ABCDE45ºF解：如图在梯形ABCD中，∵AB=CD，∠B=∠C=45º，

∴BE=AE=2cm，CF=DF=2cm，EF=AD

∴BC=BE+EF+FC=AD+4

∵MN=½（AD+BC）即5=½（AD+AD+4）

∴AD=3cm，BC=AD+4=7cmMN小结知识应用梯形ABCD的中位线长为a，高为h，则图中阴影部分的面积是多少？有一木匠想制作一个木梯，共需5根横木，其中最长端的横木长20cm，5根横木共长200cm，问其余四根分别多长？ABC