Giải thích các bước giải:
a.Ta có $AG//CD\to \widehat{FAG}=\widehat{FDC},\widehat{FGA}=\widehat{FCD}\to\Delta FAG\sim\Delta FDC(g.g)$
$\widehat{CGB}=\widehat{FCD}(BG//DC),\widehat{FDC}=\widehat{GCB}(AD//BC)\to\Delta GBC\sim\Delta CDF(g.g)$
b.Ta có $DF=3\to AF=AD-DF=BC-AF=2$
$\to \dfrac{AG}{CD}=\dfrac{AF}{DF}=\dfrac23\to AG=\dfrac23CD=\dfrac23AB=4$ (AB//CD)
$\to GB=GA+AB=10$
c.Ta có : $GA//DC\to \dfrac{GF}{FC}=\dfrac{AF}{FD}$
$\to\dfrac{GF+FC}{FC}=\dfrac{AF+FD}{FD}$
$\to\dfrac{GC}{FC}=\dfrac{AD}{FD}$
$\to AD.FC=GC.FD$
d.Ta có $AF//BC\to\dfrac{AB}{GB}=\dfrac{FC}{GC}=\dfrac{FD}{AD}(AG//DC)$
$\to GB.DF=AB.AD=AB.BC(AD=BC)$