Question

ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that: 

(i) ar (∆ADO) = ar (∆CDO) (ii) ar (∆ABP) = ar (∆CBP)

Answer 1

Given that ABCD is a parallelogram 

To prove: (i) ar (∆ADO) = ar (∆CDO) 

(ii) ar (∆ABP) = ar (∆CBP)

Proof: We know that, diagonals of a parallelogram bisect each other 

AO = OC and  BO = OD