超难数学几何题 如图,△ABC为等腰直角三角形,∠BAC=90度,D为AC的中点,AE⊥BD于E,求证∠BAE=∠FDC file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/YPJSX0N2/2010050910
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超难数学几何题 如图,△ABC为等腰直角三角形,∠BAC=90度,D为AC的中点,AE⊥BD于E,求证∠BAE=∠FDC file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/YPJSX0N2/2010050910
超难数学几何题
如图,△ABC为等腰直角三角形,∠BAC=90度,D为AC的中点,AE⊥BD于E,求证∠BAE=∠FDC
file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/YPJSX0N2/20100509105009-1849545631%5B1%5D.jpg
超难数学几何题 如图,△ABC为等腰直角三角形,∠BAC=90度,D为AC的中点,AE⊥BD于E,求证∠BAE=∠FDC file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/YPJSX0N2/2010050910
证明:
过C作AC的垂直线交AF的延长线于H
∵AB=AC
∠BAD=∠ACH ∠FAC=∠ABD
∴△ABD≌△ACH
∴AD=CH=CD ∠H=∠ADB
又∵∠ACB=∠BCH=45° CF=CF
∴△CDF≌△CHF
∴∠H=∠FDC
∴∠FDC=∠ADB=∠BAE
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