梯形ABCD AD//BC 又EH//BC 且AB AC DB DC 的延长线交EH于F,H,E ,G求证EF=GH

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梯形ABCD AD//BC 又EH//BC 且AB AC DB DC 的延长线交EH于F,H,E ,G求证EF=GH
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梯形ABCD AD//BC 又EH//BC 且AB AC DB DC 的延长线交EH于F,H,E ,G求证EF=GH
梯形ABCD AD//BC 又EH//BC 且AB AC DB DC 的延长线交EH于F,H,E ,G求证EF=GH

梯形ABCD AD//BC 又EH//BC 且AB AC DB DC 的延长线交EH于F,H,E ,G求证EF=GH
证明:△BEF∽△BDA
∴EF/AD=BF/BA
△CGH∽△CDA
∴GH/AD=CG/CD
□ABCD∽□AFGD
∴AB/AF=DC/DG
∴AB/BF=DC/CG
∴EF/AD=GH/AD
∴EF=GH