解：?$B$?為線段?$AF$?的黃金分割點(diǎn)，?$C$?為線段?$DG$?的黃金分割點(diǎn)，
矩形?$AFGD$?和矩形?$CBFG$?都是黃金矩形，證明如下：
設(shè)正方形?$ABCD$?的邊長為?$a，$?則?$AB=BC=a$?
∵點(diǎn)?$E$?是?$AB$?的中點(diǎn)
∴?$BE=\frac 12AB=\frac {a}2$?
在?$Rt△BCE$?中，∵?$BE=\frac {a}2，$??$BC=a$?
∴?$CE=\sqrt {BE^2+BC^2}=\frac {\sqrt 5}2a$?
∴?$EF=\frac {\sqrt 5}2a，$??$AF=\frac {\sqrt 5+1}2a，$??$BF=\frac {\sqrt 5-1}2a$?
∴?$\frac {AB}{AF}=\frac a{\frac {\sqrt 5+1}2a}=\frac {\sqrt 5-1}2≈0.618$?
∴點(diǎn)?$B$?是線段?$AF$?的黃金分割點(diǎn)
∵?$\frac {DC}{DG}=\frac {AB}{AF}≈0.618$?
∴點(diǎn)?$C$?是線段?$DG$?的黃金分割點(diǎn)
∵?$\frac {AD}{AF}=\frac {AB}{AF}≈0.618，$??$\frac {BF}{BC}=\frac {\frac {\sqrt 5-1}2a}{a}=\frac {\sqrt 5-1}2≈0.618$?
∴矩形?$AFGD$?和矩形?$CBFG$?都是黃金矩形
