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In Delta^(s)ABC and, AB"||"DE, BC=EF and...

In `Delta^(s)ABC and, AB"||"DE, BC=EF and BC"||"EF`. Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that
(i) ABED is a parallelogram
(ii) BCFE is a parallelogram
(iii) AC = DF
(iv) `DeltaABC~=DeltaDEF`

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