Question

In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar (△ ABC) = ar (△ ABD).

Answer 1

From the figure we know that median of a triangle divides it into triangles of equal area

We know that AO is the median of △ ACD

It can be written as

Area of △ COA = Area of △ DOA ……. (1)

We know that BO is the median of △ BCD

It can be written as

Area of △ COB = Area of △ DOB ……. (2)

By adding both the equations

Area of △ COA + Area of △ COB = Area of △ DOA + Area of △ DOB

So we get

Area of △ ABC = Area of △ ABD

Therefore, it is proved that ar (△ ABC) = ar (△ ABD).