如图,AB=AC,∠ABC=a,EC=ED,∠CED=2a,P为BD的中点连AE、PE.(1)过B作BF//DE交EP的延长线于F,求证:BF=CE(2)当a=60度时,求证:AE=2PE
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![如图,AB=AC,∠ABC=a,EC=ED,∠CED=2a,P为BD的中点连AE、PE.(1)过B作BF//DE交EP的延长线于F,求证:BF=CE(2)当a=60度时,求证:AE=2PE](/uploads/image/z/8678414-38-4.jpg?t=%E5%A6%82%E5%9B%BE%2CAB%3DAC%2C%E2%88%A0ABC%3Da%2CEC%3DED%2C%E2%88%A0CED%3D2a%2CP%E4%B8%BABD%E7%9A%84%E4%B8%AD%E7%82%B9%E8%BF%9EAE%E3%80%81PE.%EF%BC%881%EF%BC%89%E8%BF%87B%E4%BD%9CBF%2F%2FDE%E4%BA%A4EP%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%8EF%2C%E6%B1%82%E8%AF%81%EF%BC%9ABF%3DCE%282%29%E5%BD%93a%3D60%E5%BA%A6%E6%97%B6%2C%E6%B1%82%E8%AF%81%EF%BC%9AAE%3D2PE)
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如图,AB=AC,∠ABC=a,EC=ED,∠CED=2a,P为BD的中点连AE、PE.(1)过B作BF//DE交EP的延长线于F,求证:BF=CE(2)当a=60度时,求证:AE=2PE
如图,AB=AC,∠ABC=a,EC=ED,∠CED=2a,P为BD的中点连AE、PE.(1)过B作BF//DE交EP的延长线于F,求证:BF=CE(2)当a=60度时,求证:AE=2PE
如图,AB=AC,∠ABC=a,EC=ED,∠CED=2a,P为BD的中点连AE、PE.(1)过B作BF//DE交EP的延长线于F,求证:BF=CE(2)当a=60度时,求证:AE=2PE
把三角形ACE绕A点逆时针旋转,使得C点和B点重合,E点旋转后对应的点为C',连接C'E和BD交于F点
AC'=AE
角C'AE=60
三角形AC'E为等边三角形
角AC'E=角AEC'=60
∠AC'B+∠BC'F=∠AEC+∠DEF
∠BC'F=∠DEF
△C'BF≌△EDF
BF=FD
C'F=FE
F是BD的中点
P也是BD的中点
所以F和P点重合,BE和PE重合
F(P)是BE的中点
AF(AP)⊥BE
∠AEF(P)=60
AE=2PE.