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D, E and F are respectively the mid-poi...

D, E and F are respectively the mid-points of the sides BC, CA and AB of a`DeltaA B C`. Show that
(i) BDEF is a parallelogram.
(ii) `a r\ (D E F)=1/4a r\ (A B C)`
(iii) `a r\ (B D E F)=1/2a r\ (A B C)`

Text Solution

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i) In ΔABC, D and E are the mid-points of side BC and AC respectively.
Therefore, the line joining points D and E will be parallel to line AB and also half of it as per the midpoint theorem.
The mid-point of AB is Fand E is the mid-point of AC
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