\( D, E \) and \( F \) are respectively the mid-points of the sides \( \mathrm{BC}, \mathrm{CA} ...

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\( D, E \) and \( F \) are respectively the mid-points of the sides \( \mathrm{BC}, \mathrm{CA} \) and \( \mathrm{AB} \) of a \( \triangle \mathrm{ABC} \).
Show that
P
(i) BDEF is a parallelogram.
(ii) \( \operatorname{ar}(\mathrm{DEF})=\frac{1}{4} \operatorname{ar}(\mathrm{ABC}) \)
- (iii) \( \operatorname{ar}(\mathrm{BDEF})=\frac{1}{2} \operatorname{ar}(\mathrm{ABC}) \)
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