如图1,△ABC中,AB>AC,AD平分∠BAC交BC于点D,在AB上截取AE=AC,过点E作EF∥BC交AD于点F.
问题描述:
如图1,△ABC中,AB>AC,AD平分∠BAC交BC于点D,在AB上截取AE=AC,过点E作EF∥BC交AD于点F.
①△ADE≌△ADC
②∠EDF=∠EFD
(2)如图2,△ABC中,AB>AC,AD平分△的外角∠EAC交BC的延长线于点D,在AB的反向延长线上截取AE=AC,过点E作EF∥BD交AD的反向延长线于点F.求证:四边形CDEF是菱形;
(3)如图3在(2)的条件下,若△ABC为等腰三角形,且四边形FCDE为正方形,求∠B的度数;设EF=1,FG=X,求满足题目条件的X值.
答
(1)证明:①在△AEF和△ACF中,∵AE=AC,∠EAF=∠CAF,AD=AD,∴△ADE≌△ADC;②∵△ADE≌△ADC,∴DE=DC,∠ADE=∠ADC同理△AFE≌△AFC,∴EF=CF∵EF∥BC∴∠EFD=∠ADC,∴∠EFD=∠ADE,∴DE=EF,∴DE=EF=CF=DC,∴四边形CD...