$證明：(1)∵AD是△ABC的角平分線$
$∴∠BAD=∠CAD$
$由作圖知AE=AF$
$在△ADE和△ADF 中$
$\begin{cases}{AE=AF}\\{∠BAD=∠CAD}\\{AD=AD}\end{cases}$
$∴△ADE≌△ADF(\mathrm {SAS})$
$(2)∵∠BAC= 80°，AD 為△ABC 的角平分線$
$∴∠EAD= \frac{1}{2}∠BAC=40°$
$由作圖知，AE=AD，∴∠AED=∠ADE$
$∴∠ADE=\frac{1}{2}×(180°-40°)=70°$
$∵AB=AC，∴AD⊥BC$
$∴∠BDE=90°-∠ADE=20°$
