已知:如图,△ABC中,AB=AC,AD⊥BC且垂足为点D.将△ADC绕点D逆时针旋转90°后,点A落在BD上点A1处,点C落在DA延长线上C1处,A1C1与AB交于点E.求证:△A1BE≡△AC1E

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已知:如图,△ABC中,AB=AC,AD⊥BC且垂足为点D.将△ADC绕点D逆时针旋转90°后,点A落在BD上点A1处,点C落在DA延长线上C1处,A1C1与AB交于点E.求证:△A1BE≡△AC1E
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已知:如图,△ABC中,AB=AC,AD⊥BC且垂足为点D.将△ADC绕点D逆时针旋转90°后,点A落在BD上点A1处,点C落在DA延长线上C1处,A1C1与AB交于点E.求证:△A1BE≡△AC1E
已知:如图,△ABC中,AB=AC,AD⊥BC且垂足为点D.将△ADC绕点D逆时针旋转90°后,点A落在BD上点A1处,点C落在DA延长线上C1处,A1C1与AB交于点E.求证:△A1BE≡△AC1E

已知:如图,△ABC中,AB=AC,AD⊥BC且垂足为点D.将△ADC绕点D逆时针旋转90°后,点A落在BD上点A1处,点C落在DA延长线上C1处,A1C1与AB交于点E.求证:△A1BE≡△AC1E
∵ AB=AC,AD⊥BC
∴ AD分△ABC为两个全等RT△
又 RT△A1DC1是由RT△ADC旋转90°而来
∴ ∠C1=∠B、BD=C1D、AD=A1D
∴ A1D=AC1 (BD-AD=C1D-A1D)
∴ 在 △A1BE、△AC1E中
A1D=AC1 、∠C1=∠B、∠E=∠E(对顶)
∴ △A1BE≌△AC1E