D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar(ΔBOE) = ar(Δ ABC)
Join A and D to get AD median
(Median divides the triangle into two triangles of equal area)
Therefore,
Area (ABD) = Area (ABC)
Now,
Join A and E to get AE median
Similarly,
We can prove that,
Area (ABE) = Area (ABD)
Area (ABE) = ABC (Area (ABD) = Area (ABC) (i)
Join B and O and we get BO median
Now,
Area (BOE) = Area (ABE)
Area (BOE) = * Area (ABC)
Area (BOE) = Area (ABC)