解：?$(1)$?∵?$AD=2，$??$AE=1，$??$∠DAE=90°$?
∴?$DE=\sqrt 5$?
∴?$EH=\sqrt 5，$??$AF=AH=\sqrt 5-1，$??$DF=2-(\sqrt 5-1)=3-\sqrt 5$?
?$(2)$?由?$AF^2=(\sqrt 5-1)^2=6-2\sqrt 5$?
?$AD · DF=2(3-\sqrt 5)=6-2\sqrt 5$?
∴?$AF^2=AD · DF，$?即?$\frac {AF}{AD}=\frac {DF}{AF}$?
∴點(diǎn)?$F$?是?$AD$?的黃金分割點(diǎn)
