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Q : 3    Show that the diagonals of a parallelogram divide it into four triangles of equal area.

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Let ABCD is a parallelogram. So, AB || CD and AD || BC and we know that Diagonals bisects each other. Therefore, AO = OC and BO = OD

Since OD = BO 
Therefore, ar (\DeltaBOC) = ar (\DeltaDOC)...........(a)   ( since OC is the median of triangle CBD)

Similarly, ar(\DeltaAOD) = ar(\DeltaDOC) ............(b)     ( since OD is the median of triangle ACD)

and, ar (\DeltaAOB) = ar(\DeltaBOC)..............(c)           ( since OB  is the median of triangle ABC)

From eq (a), (b) and eq (c), we get

  ar (\DeltaBOC) = ar (\DeltaDOC)= ar(\DeltaAOD) =  (\DeltaAOB)

Thus, the diagonals of ||gm divide it into four equal triangles of equal area.

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