O is any point on the diagonal BD of the parallelogram ABCD. Prove that ar (OAB) = ar (OBC).
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Since both the triangles have bases in ratio which is in inverse of the ratio of their heights , that is
b1/b2=h2/h1 hence their area must be same
A1=1/2b1*h1=1/2b1*h1/b2*b2= 1/2b2*h2 (since b1/b2=h2/h1 )= A2
b1/b2=h2/h1 hence their area must be same
A1=1/2b1*h1=1/2b1*h1/b2*b2= 1/2b2*h2 (since b1/b2=h2/h1 )= A2
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