梯形中位線的證明

BACEF三角形中位線定理三角形的中位線平行于第三邊，并且等于它的一半即EF//BC，EF=?BCM梯形中位線定理梯形的中位線平行于兩底，并且等于兩底和的一半BCAEDF已知：梯形ABCD中，AD//BC，AE=EB，DF=FC求證：EF//BC，EF=?（BC+AD）證明：連結(jié)AF并延長(zhǎng)，交BC的延長(zhǎng)線于點(diǎn)M∵DF=FC，∠1=∠2，∠D=∠3，∴?ADF≌?MCF∴AF=MF，AD=CM又AE=EB∴EF是?ABM的中位線∴EF//BC，EF=?BM∵BM=BC+CM=BC+AD∴EF=?（BC+AD）1231BACDEFGBACDEFNMBACDEFMNBACDEFGBACDEFGBACDEFNMBACDEFGBACDEFMNBACDEFGBACDEFGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFNMBACDEFBACDEFNMMNGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFMNBACDEFBACDEFNMMNBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMMNBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMMNBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFGBACDEFBACDEFNMGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFGBACDEFBACDEFMNGBACDEFGBACDEFBACDEFNMGBACDEFBACDEFBACDEFNMMNGBACDEFGBACDEFBACDEFMNGBACDEFBACDEFBACDEFNMMNG知識(shí)鞏固1梯形的上底長(zhǎng)8，下底長(zhǎng)10，則這個(gè)梯形的中位線長(zhǎng)＿＿2梯形的上底長(zhǎng)8，中位線長(zhǎng)10，則下底長(zhǎng)是＿＿3已知等腰梯形中位線長(zhǎng)6cm，它的腰長(zhǎng)5cm，則這個(gè)梯形的周長(zhǎng)為＿＿＿cm4一個(gè)等腰梯形周長(zhǎng)80，如果它的中位線與腰長(zhǎng)相等，它的中位線長(zhǎng)＿＿91222205梯形的中位線長(zhǎng)9cm，一條對(duì)角線把中位線分成1:2兩部分，則該梯形的下底長(zhǎng)＿＿＿cm12例：一個(gè)等腰梯形的高是2，它的中位線長(zhǎng)5，一個(gè)底角為45o，求這個(gè)梯形的上底，下底的長(zhǎng)？ABCDE45oF解：如圖在梯形ABCD中，∵AB=CD，∠B=∠C=45o，

∴BE=AE=2cm，CF=DF=2cm，EF=AD

∴BC=BE+EF+FC=AD+4

∵M(jìn)N=?（AD+BC）即5=?（AD+AD+4）

∴AD=3cm，BC=AD+4=7cmMN小結(jié)知識(shí)應(yīng)用梯形ABCD的中位線長(zhǎng)為a，高為h，則圖中陰影部分的面積是多少？有一木匠想制作一個(gè)木梯，共需5根橫木，其中最長(zhǎng)端的橫木長(zhǎng)20cm，5根橫木共長(zhǎng)200cm，問(wèn)其余四根分別多長(zhǎng)？ABC