Mathematics
In the figure (3) given below, ABCD is a parallelogram. O is any point on the diagonal AC of the parallelogram. Show that the area of ∆AOB is equal to the area of ∆AOD.
Theorems on Area
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Answer
Join BD, which meets AC at P.
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 …….(i)
Similarly,
PO is median of ∆BOD,
∴ Area of ∆BOP = Area of ∆POD …….(ii)
Now, adding (i) and (ii), and 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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