解：?$(1)BD$?和?$BC$?相等，理由如下：
∵?$AC⊥CB$?，?$DB⊥CB$?
∴?$∠ACB=∠DBE=90°$?
∵?$AB⊥DE$?
∴?$∠DEB+∠FBE=90°$?
∵?$∠D+∠DEB=90°$?
∴?$∠D=∠ABC$?
在?$△ABC$?與?$△EDB$?中
?$\begin {cases}{∠C=∠DBE}\\{∠ABC=∠D}\\{AB=DE}\end {cases}$?
∴?$△ABC≌△EDB(\mathrm {AAS})$?
∴?$BD=BC$?
?$(2)$?∵?$△ABC≌△EDB$?
∴?$BC=BD=6\ \mathrm {cm}$?，?$AC=BE$?
∵?$E$?是?$BC$?的中點(diǎn)
∴?$BE=CE=\frac {1}{2}BC=3\ \mathrm {cm}$?
∴?$AC=BE=3\ \mathrm {cm}$?
