(1) 理由：因为$a// b，$所以$\angle BAC=\angle ACF，$$\angle BAD+\angle ABE = 180^{\circ}。$
又因为$AC$平分$\angle BAD，$所以$\angle BAD = 2\angle BAC。$
$\triangle ABC$平移得到$\triangle DEF，$所以$\angle ACB=\angle DFE，$而$\angle BAC=\angle ACB，$所以$\angle BAD = 2\angle DFE。$
(2) 因为$\triangle ABC$平移得到$\triangle DEF，$$AD = BE=CF = 1.5\mathrm{cm}，$$\triangle ABC$的周长$C_{\triangle ABC}=AB + BC+AC = 9\mathrm{cm}。$
四边形$ABFD$的周长$C_{ABFD}=AB + BF+FD+DA=AB+(BC + CF)+(AC)+DA=(AB + BC + AC)+2AD=9 + 2\times1.5=12\mathrm{cm}。$
