In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF.

[question] Question. In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that (i) Quadrilateral ABED is a parallelogram (ii) Quadrilateral BEFC is a parallelogram (iii) $A D \| C F$ and $A D=C F$ (iv) Quadrilateral ACFD is a parallelogram (v) $\mathrm{AC}=\mathrm{DF}$ (vi) $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$ [/question] [solution] Solution: (i) It is given that $A B=D E$ and $...