$证明:∵AB⊥BD,ED⊥BD,AC⊥CE,$ $ ∴∠B=∠D=∠ACE=90°,$ $ ∴∠DCE+∠DEC=90°,∠BCA+∠DCE=90°,$ $ ∴∠BCA=∠DEC.$ $在△ABC和△CDE中，\ $ $\begin{cases}{∠BCA=∠DEC,}\\{∠B=∠D,}\\{ AB=CD,}\end{cases}$ $ ∴△ABC≌△CDE(\mathrm {AAS}).$ $证明:(2)∵△ABE≌△ACD,$ $∴AB=AC.$ $ ∵AD=AE,$ $∴BD=CE.$ $在△BOD和△COE中，$ $\begin{cases}{∠B=∠C,}\\{∠BOD=∠COE, }\\{ BD=CE,}\end{cases}$ $ ∴△BOD≌△COE(\mathrm {AAS}).$ （更多请点击查看作业精灵详解）
$证明:(1)∵∠A=∠ABC,$ $∠ABC=∠GBH,\ $ $∴∠A=∠GBH.\ $ $∵EF⊥AB,GH⊥AB,$ $∴∠AFE=∠BHG.\ \ $ $在△AEF和△BGH中,\ $ $\begin{cases}{∠A=∠GBH，}\\{∠AFE=∠H,\ }\\{EF=GH,\ }\end{cases}$ $∴△AEF≌△BGH(\mathrm {AAS}).$（更多请点击查看作业精灵详解）
$证明:(1)在△ACE和△BDF中,$ $\begin{cases}{∠A=∠B\ }\\{∠ACE=∠BDF,\ }\\{AE=BF,\ }\end{cases}$ $∴△ACE≌△BDF(\mathrm {AAS}).$ $(2)由(1)知△ACE≌△BDF,$ $∴BD=AC=2.$ $ ∵AB=8,$ $∴CD=AB-AC-BD=4.$ $证明: ∵AB//DE,$ $∴∠B=∠DEF.\ \ $ $在△ABC和△DEF中,\ $ $\begin{cases}{∠ACB=∠F,}\\{∠B=∠D}\\{EF=DE,\ }\end{cases}$ $∴△ABC≌△DEF(\mathrm {AAS}).$
$证明:(1)在△ABE和△ACD中，\ $ $∠A=∠A,$ $∠B=∠C,\ $ $AE=AD,\ $ $∴△ABE≌△ACD(\mathrm {AAS}).$
$解:(2)∵△AEF≌△BGH,\ $ $∴AF=BH，$ $∴AB=FH=4.\ $ $∵EF⊥AB,GH⊥AB,$ $∴∠EFD=∠GHD.\ $ $在△EFD和△GHD中，\ $ $\begin{cases}{∠EDF=∠GDH,\ }\\{EF=GH,\ }\\{∠EFD=∠GHD,\ }\end{cases}$ $∴△EFD≌△GHD(\mathrm {AAS}),\ $ $∴DH=DF=\frac{1}{2}FH=\frac{1}{2}AB=2.\ $
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