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In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = ar(ABC).
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1
AD is a median of 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
ar (ΔBED) = ar (ΔBAE) and ar (ΔBED) = 1/2 ar(ΔABD)
ar (ΔBED) = 1/2 × [1/2 ar(ABC)] (Using equation (i))
∴ ar (ΔBED) = 1/4 ar(ΔABC)
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