In a triangle ABC, E is the mid-point of median AD. Show that `a r (B – InterviewSolution

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1.	In a triangle ABC, E is the mid-point of median AD. Show that `a r (B E D)=1/4a r (A B C)```
Answer» We know, the median of a triangle, divides the triangle into two triangles of equal areas. So, in `Delta ABC` `ar(ACD)=ar(ABD) = 1/2ar(ABC)->(1)` Also, we are given,`E` is the mid-point of `AD` that means `BE` is the median of `Delta ABD` So, `ar(BED)=ar(AEB) = 1/2ar(ABD)` From (1), `ar(BED) = 1/2(1/2ar(ABC))` `ar(BED) = 1/4ar(ABC)`

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