(1)∵AB=AC,AD=AE,∠BAC=∠DAE=60°, ∴△AED和△ABC为等边三角形, ∴∠C=∠ABC=60°,∠EAB=∠DAC, ∴△EAB≌△DAC, ∴∠EBA=∠C=60°, ∵EF∥BC, ∴∠EFB=∠ABC=60°, ∵在△EFB中,∠EFB=∠EBA=60°, ∴△EFB为等边三角形,
(2)①△BEF为等腰三角形, ∵AB=AC,AD=AE,∠BAC=∠DAE, ∴△AED和△ABC为等腰三角形, ∴∠C=∠ABC,∠EAB=∠DAC, ∴△EAB≌△DAC, ∴∠EBA=∠C, ∵EF∥BC, ∴∠EFB=∠ABC, ∵在△EFB中,∠EFB=∠EBA, ∴△EFB为等腰三角形, ②AB=AC,点D为射线BC上一个动点(不与B、C重合),以AD为一边向AD的左侧作△ADE,使AD=AE,∠DAE=∠BAC,过点E作BC的平行线,交直线AB于点F,连接BE. ∵△BEF为等腰三角形, ∵AB=AC,AD=AE,∠BAC=∠DAE, ∴△AED和△ABC为等腰三角形, ∴∠ACB=∠ABC,∠EAB=∠DAC, ∴△EAB≌△DAC, ∴∠EBA=∠ACD, ∴∠EBF=∠ACB, ∵EF∥BC, ∴∠AFE=∠ABC, ∵∠ABC=∠ACB, ∴∠AFE=∠ACB, ∵在△EFB中,∠EBF=∠AFE, ∴△EFB为等腰三角形.
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