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

The Figure given in question does not match what the question says here is the correct figure according to the question

Consider ΔACD

AO is the median which divides the area(ΔACD) into two equal parts

area(ΔAOD) = area(ΔAOC) …(i)

Consider ΔBCD

BO is the median which divides the area(ΔBCD) into two equal parts

area(ΔBOD) = area(ΔBOC) …(ii)

area(ΔAOD) + area(ΔBOD) = area(ΔAOC) + area(ΔBOC) …(iii)

From figure

area(ΔAOD) + area(ΔBOD) = area(ΔABD) and

area(ΔAOC) + area(ΔBOC) = area(ΔABC)

therefore equation (iii) becomes

area(ΔABD) = area(ΔABC)

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