Q. 34.4( 37 Votes )

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)


Answer :

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)


Add equation (i) and (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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