Question

ABCD us a paralleligram. The diagnols AC and BD intersect each other at 'O'. Prove that ar(TriangleAOD)=ar(TrianlrBOC).

Answer 1

let in parallelogram abcd

ac and bd are diagonals

and met at o

hence ao=oc

and do=ob

(o bisect the diagonal)

proof:

let in triangle aod and triangle boc

seg ad=seg bc(opposite side of parallelogram are equal)

.....1

seg do=seg ob(o bisect the diagonal)

....2

and seg ao= seg oc (o bisect the diagonal)....3

from 1 ,2 and 3

triangle aob= triangle boc

thus there areas be same

hence area(traingle aob)= areap(triangle boc)