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ABC is the triangle and AD be the median (which means BD =DC).
Construct AN perpendicular (90 degree) to BC.
Now ar(ABD) = ½ AN x BD [1]
ar(ACD) = ½ AN x CD [2]
We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD) => Median of a triangle divides it into two triangles of equal area.
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