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 ar(ABC) = ar (ABD).
Given ΔABC and ΔABD are two triangles on the same base AB. To show : ar(ABC)=ar(ABD) Proof : Since the line segment CD is bisected by AB at O. OC=OD. In ΔACD, We have OC=OD. So, AO is the median of ΔACD Also we know that median divides a triangle into two triangles of equal areas. ∴ar(ΔAOC)=ar(ΔAOD) _______ (1) Similarly , In ΔBCD, BO is the median. (CD bisected by AB at O) ∴ar(ΔBOC)=ar(ΔBOD) _______ (2) On adding equation (1) and (2) we get, ar(ΔAOC)+ar(ΔBOC)=ar(ΔAOD)+ar(ΔBOD) ∴ar(ΔABC)=ar(ΔABD)
