证明：延长BA、CE交于F∵∠BAC=90°，BE⊥CF，∠ADB=∠CDE∴∠CAF=90°，∠ABD=∠ACF∵在△BAD和△CAF中， ∠ABD=∠ACF，AB=AC，∠BAC=∠CAF∴△BAD≌△CAF（ASA）∴BD=CF∵BE是∠ABC的平分线，BE⊥CF∴CE=EF，即CF=2CE∴BD=2CE
