prove that . In an triangle ABC , E is the mid point of median AD ?
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We know that the median of a triangle divides it into two triangles of equal areas. AD is a median for triangle ABC and BE is the median of ΔABD.
Since AD is the median of ΔABC, so it will divide ΔABC into two equal triangles.
∴ ar (ΔABD) = ar (ΔADC)
Also, ar (ΔABD) = 1/2 ar(ABC) ___(i)
Now, In ΔABD, BE is the median,
Therefore, BE will divide ΔABD into two equal triangles
area (ΔBED) = area (ΔBAE) and area (ΔBED) = 1/2 area(ΔABD)
area(ΔBED) = 1/2 × [1/2 ar(ABC)] (Using equation (i))
∴ area (ΔBED) = 1/4 ar(ΔABC)
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