Q : 4 In Fig. , ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that .
We have, ABC and ABD on the same base AB. CD is bisected by AB at point O.
OC = OD
Now, in ACD, AO is median
ar (AOC) = ar (AOD)..........(i)
Similarly, in BCD, BO is the median
ar (BOC) = ar (BOD)............(ii)
Adding equation (i) and eq (ii), we get
ar (AOC) + ar (BOC) = ar (AOD) + ar (BOD)