# Prove that the diagonals of parallelogram divides it into 4 triangle of equal area

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The Brainliest Answer!

as we know that the diagonals of a ║gm divide it into two triangles of equal areas, so

ar. (ADC) = ar. (BDC)

now, in tri. ADC, OD is the median so,

ar. ( AOD) = ar. (AOB ) ....1

similarly, ar. (COD) = ar. (BOC) ....2

NOW, ar. (ADC) = ar. (BDC)

⇒ 1/2 ar.(ADC) = 1/2 ar. (BDC)

from 1 and 2,

ar. (AOD) = ar. (AOB) = ar. (COD) = ar. (BOC)

hence, proved.

In ΔADC

OD is the median

∴ar DOA = ar DOC ________ (1)

similarly in ΔADB ,OA i s the median

∴ar DOA = ar BOA________________(2)

similarly we can prove

ar AOB = ar BOC_______________(3)

and

ar BOC = ar DOC _______________(4)

from 1 , 2 , 3 and 4

we get

ar (DOC)= ar(DOA)=ar(AOB)= ar(BOC)