(i) From the figure we know that △ DBE and △ DCE lie on the same base DE between the parallel lines BC and DE.
So we get
Area of △ DBE = Area of △ DCE ……. (1)
By adding △ ADE both sides
Area of △ DBE + Area of △ ADE = Area of △ DCE + Area of △ ADE
We get
Area of △ ABE = Area of △ ACD
Therefore, it is proved that ar (△ ACD) = ar (△ ABE).
(ii) Subtracting △ ODE from equation (1)
We get
Area of △ DBE – Area of △ ODE = Area of △ DCE – Area of △ ODE
We get
Area of △ OBD = Area of △ OCE
Therefore, it is proved that ar (△ OCE) = ar (△ OBD).