解:(1)CF与BD位置关系是垂直,证明如下:如图(1)∵AB=AC,∠ACB=45°,∴∠ABC=45°,由正方形ADEF得AD=AF, ∵∠DAF=∠BAC=90°,∴∠DAB=∠FAC,∴△DAB≌△FAC,∴∠ACF=∠ABD∴∠BCF=∠ACB+∠ACF=90°,即CF⊥BD;
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