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Question
ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove
that: (1) ar (ΔADO) = ar (ΔCDO) (2) ar (ΔABP) = ar (ΔCBP)
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Solution
Given that ABCD is a parallelogram
To prove: (1) ar (ΔADO) = ar (ΔCDO)
(2) ar ( ΔABP) = ar (ΔCBP)
Then area (ΔADO) = area (ΔCDO)
Then; area (ΔBAO) area (ΔBCO) ......(1)
In a ΔPAC, Since PO is a median
Then, area (ΔPAO) = area (ΔPCO) ......(2)
⇒ Area (ΔABP) = Area of ΔCBP
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