Given In figure AB || DE and AC || DF, also AB = DE and AC = DF To prove BC ||EF and BC = EF Proof In quadrilateral ABED, AB||DE and AB = DE So, ABED is a parallelogram. AD || BE and AD = BE Now, in quadrilateral ACFD, AC || FD and AC = FD …..(i) Thus, ACFD is a parallelogram. AD || CF and AD = CF …(ii) From Eqs. (i) and (ii), AD = BE = CF and CF || BE …(iii) Now, in quadrilateral BCFE, BE = CF and BE||CF [from Eq. (iii)] So, BCFE is a parallelogram. BC = EF and BC|| EF . Hence proved.