In `DeltaA B C`and `DeltaD E F`, `A B\ =\ D E`, `A B\ ||\ D E`, `B C\ =\ E F` and `B C\ ||\ E F`. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).Show that
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ∆ ABC ≅ ∆ DEF.