RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与直线
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![RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与直线](/uploads/image/z/10898697-57-7.jpg?t=RT%E2%96%B3ABC%E4%B8%ADAB%EF%BC%9DAC%2C%E7%82%B9D%E3%80%81E%E6%98%AF%E7%BA%BF%E6%AE%B5AC%E4%B8%8A%E4%BF%A9%E7%82%B9%2C+AD%EF%BC%9DEC%2CAM%E2%8A%A5BD%2C%E5%9E%82%E8%B6%B3%E4%B8%BAM%2CAM%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4%E4%B8%8EBC%E4%B8%8A%E4%B8%80%E7%82%B9N%2C%E7%9B%B4%E7%BA%BFBD%E4%B8%8ERT%E2%96%B3ABC%E4%B8%ADAB%EF%BC%9DAC%2C%E7%82%B9D%E3%80%81E%E6%98%AF%E7%BA%BF%E6%AE%B5AC%E4%B8%8A%E4%BF%A9%E7%82%B9%2C+++++AD%EF%BC%9DEC%2CAM%E2%8A%A5BD%2C%E5%9E%82%E8%B6%B3%E4%B8%BAM%2CAM%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4%E4%B8%8EBC%E4%B8%8A%E4%B8%80%E7%82%B9N%2C%E7%9B%B4%E7%BA%BFBD%E4%B8%8E%E7%9B%B4%E7%BA%BF)
RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与直线
RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与
RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与直线NE相交于点F.
试判断△DEF的形状,并加以证明.
RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与RT△ABC中AB=AC,点D、E是线段AC上俩点, AD=EC,AM⊥BD,垂足为M,AM的延长线交与BC上一点N,直线BD与直线
△DEF是等腰三角形.
证明:如图,过点C作CP⊥AC,交AN延长线于点P
∵Rt△ABC中AB=AC,∴∠BAC=90°,∠ACB=45°,
∴∠PCN=∠ACB,∠BAD=∠ACP
∵AM⊥BD,
∴∠ABD+∠BAM=∠BAM+∠CAP=90°
∴∠ABD=∠CAP
∴△BAD≌△ACP
∴AD=CP,∠ADB=∠P
∵AD=CE,∴CE=CP
∵CN=CN
∴△CPN≌△CEN
∴∠P=∠CEN,∴∠CEN=∠ADB,∴∠FDE=∠FED
∴ △DEF是等腰三角形