In the following figure, DE is parallel to BC. Show that :

(i) Area (△ ADC) = Area (△ AEB)

(ii) Area (△ BOD) = Area (△ COE)

We know that,

Triangles on the same base and between the same parallel lines are equal in area.

Since, triangle DEB and DEC lie on the same base DE and between the same parallel lines DE and BC.

∴ Area of △ DEC = Area of △ DEB ………(1)

(i) Adding area of △ ADE in both sides of the equation (1), we get :

⇒ Area of △ DEC + Area of △ ADE = Area of △ DEB + Area of △ ADE

⇒ Area of △ ADC = Area of △ AEB.

Hence, proved that area of △ ADC = area of △ AEB.

(ii) Subtracting area of △ DOE in both sides of the equation (1), we get :

⇒ Area of △ DEC - Area of △ DOE = Area of △ DEB - Area of △ DOE

⇒ Area of △ COE = Area of △ BOD.

Hence, proved that area of △ BOD = area of △ COE.