a) Xét $\Delta DAI$ và $\Delta ABC$ có:
$DA=AB$
$\widehat{IDA}=\widehat{CAB}$ (cùng bù $\widehat{DAE}$)
$DI=AC$
$\Rightarrow $$\Delta DAI=\Delta ABC$
$\Rightarrow AI=BC$
b) Gọi $IA\cap BC=H$
$\widehat{DAI}=\widehat{ABC}$
Mà $\widehat{DAI}+\widehat{BAH}=90^o$
$\Rightarrow \widehat{ABC}+\widehat{BAH}=90^o$
$\Rightarrow \widehat{AHB}=90^o$
$\Rightarrow IA\bot BC$
