Cách 1:
Ta có:
$\quad S_{ABD} = S_{ABC} = \dfrac12AB\cdot AD$
$\Leftrightarrow S_{AOB} + S_{AOD} = S_{AOB} + S_{BOC}$
$\Leftrightarrow S_{AOD} = S_{BOC}$
Cách 2:
Ta có:
$AB//CD$
$\Rightarrow \triangle AOB\backsim \triangle COD$
$\Rightarrow \dfrac{OA}{OC}= \dfrac{OB}{OD}$
Ta lại có:
$\quad \dfrac{S_{AOD}}{S_{BOC}} = \dfrac{\dfrac12OA\cdot OD}{\dfrac12OB\cdot OC}$
$\Leftrightarrow \dfrac{S_{AOD}}{S_{BOC}}= \dfrac{OA}{OC}\cdot \dfrac{OD}{OB}$
$\Leftrightarrow \dfrac{S_{AOD}}{S_{BOC}}= \dfrac{OB}{OD}\cdot\dfrac{OD}{OB}$
$\Leftrightarrow \dfrac{S_{AOD}}{S_{BOC}}=1$
$\Leftrightarrow S_{AOD} = S_{BOC}$
