Mathematics
In the adjoining figure, ABCD is a parallelogram and O is any point on its diagonal AC. Show that : ar (ΔAOB) = ar (ΔAOD).
Theorems on Area
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Answer
In ∆ABD, AP is the median (As P is mid-point of BD because diagonals of ||gm bisect each other).
Since, median of triangle divides it into two triangles of equal area.
∴ Area of ∆ABP = Area of ∆ADP ……(1)
Similarly,
PO is median of ∆BOD,
∴ Area of ∆BOP = Area of ∆POD ……(2)
Now, adding equations (1) and (2), we get :
⇒ Area of ∆ABP + Area of ∆BOP = Area of ∆ADP + Area of ∆POD
⇒ Area of ∆AOB = Area of ∆AOD.
Hence, proved that area of ∆AOB = area of ∆AOD.
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