Prove that the median of a triangle divides it into two triangles whose areas are equal

Draw a height from point B.
BE Height – The total height for the triangles BAD and BCD.
SBAD = BE * AD / 2
SBCD = BE * DC / 2
AD = DC (median by definition)
SBAD / SBCD = (BE * AD / 2) / (BE * DC / 2) = BE * AD / BE * DC = AD / DC = 1
SBAD = SBCD

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