Question

ΔABC and ΔABD 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

given:- CO=OD

to prove:-ar (ABC)=ar (ABD)
proof:-In triangle ABC
area=1/2×b×h
=CO×AB........1
similarly in triangle ABD
area=1/2×OD×AB............2
from 1 and 2 we get
ar of ABC=ar of ABD

Answer 2

In triangle ABC, AO is the median (CD is bisected by AB at O)

So, ar(AOC)=ar(AOD)..........(i)

Also,

triangle BCD,BO is the median. (CD is bisected by AB at O)

So, ar(BOC) = ar(BOD)..........(ii)

Adding (i) and (ii),

We get,

ar(AOC)+ar(BOC)=ar(AOD)+ar(BOD)

⇒ ar(ABC) = ar(ABD)

Hence showed.