$證明：(1)∵?AC⊥BC$
$?∴?∠ACB=90°=∠E?$
$在?Rt△ABC?和?Rt△ADE?中$
$?\begin{cases}{AB=AD}\\{BC=DE}\end{cases}?$
$∴?Rt△ABC≌Rt△ADE(\mathrm {HL})?$
$∴?AC=AE?$
$?(2)?延長?AF、??BC?交于點?G?$
$∵?△ABC≌ △ADE?$
$∴?∠BAC=∠DAE?$
$又?∠ABC=∠CAD?$
$∴?∠CAE=∠CAD+∠DAE$
$=∠ABC+∠BAC= 90°=∠ACB?$
$∴?BG//AE?$
$∴?∠G= ∠EAG?$
$在?△AEF ?和?△GBF ?中$
$?\begin{cases}{∠AFE=∠GFB}\\{∠EAF=∠BGF}\\{EF=BF}\end{cases}?$
$∴?△AEF≌△GBF(\mathrm {AAS})?$
$∴?AE=BG $
$∵?AC=AE，?∴?BG=AC$
$在?△ABG ?和?△DAC ?中$
$?\begin{cases}{AB=DA}\\{∠ABG=∠DAC}\\{BG=AC}\end{cases}?$
$∴?△ABG≌ △DAC(\mathrm {SAS})?$
$∴?∠G = ∠ACD?$
$∵?∠ACG=∠ACB=90°，?即?∠ACD+∠GCD=90°?$
$∴?∠G+∠GCD=90°，?∴?AF⊥CD?$
