1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM

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1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM1.已知:如图,AB//CD,EN//CA,EM//DB

1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM
1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM

1.已知:如图,AB//CD,EN//CA,EM//DB.求证AN=BM
∵DC‖AB
∴∠ADC=∠EAN
∵NE‖AC
∴∠NEA=∠DAC
∴△ANE∽△DAC
∴AN:DC=AE:AD
∵DC‖AB
∴AE:AD=BE:BC
∴AN:DC=BE:BC
∵EM‖BD
∴∠MEB=∠CBD
∵DC‖AB
∴∠DCB=∠EBM
∴△BEM∽△CBD
∴BE:BC=BM:CD
∵AN:DC=BE:BC(已证)
∴BM:CD=AN:CD(等量代换)
∴AN=BM