已知:梯形abcd,dc平行ab,在下底ab上取ae=ef,连接de,cf并延长交于点g,ac与dg交于点M求证DG*ME=EG*DM

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已知:梯形abcd,dc平行ab,在下底ab上取ae=ef,连接de,cf并延长交于点g,ac与dg交于点M求证DG*ME=EG*DM
已知:梯形abcd,dc平行ab,在下底ab上取ae=ef,连接de,cf并延长交于点g,ac与dg交于点M求证DG*ME=EG*DM

已知:梯形abcd,dc平行ab,在下底ab上取ae=ef,连接de,cf并延长交于点g,ac与dg交于点M求证DG*ME=EG*DM
已知:梯形ABCD,DC‖AB,在下底AB上取AE=EF,连接DE,CF并延长交于点G,AC与DG交于点M,求证DG×ME=EG×DM
证明:∵DC‖AB
∴△AME∽△CMD,△EFG∽△DCG
∴ME/DM=AE/DC=EF/DC=EG/DG
∴ME/DM=EG/DG
∴DG×ME=EG×DM

dg*me=eg*dm
eg/dg=me/dm
因为EG/DG=EF/CD
ME/DM=AE/CD
AE=EF
所以EG/DG=ME/DM
DG*ME=EG*DM

DC||AB => △DMC∽△EMA①, △DGC∽△EGF ②
① => DM/ME=DC/EA, 又AE=EF, => DM/ME=DC=EF ③
② => DC/EF=DG/EG ④
③④ => DM/ME=DG/EG => DG*ME=EG*DM