**Given :** In DABC and DDEF, AB = DE, AB ||DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F.

**To Prove :** (i) ABED is a parallelogram

(ii) BEFC is a parallelogram

(iii) AD || CF and AD = CF

(iv) ACFD is a parallelogram

(v) AC = DF

(vi) ∆ABC ≅ ∆DEF

**Proof :** (i) In quadrilateral ABED, we have

AB = DE and AB || DE. [Given]

⇒ ABED is a parallelogram. [One pair of opposite sides is parallel and equal]

(ii) In quadrilateral BEFC, we have

BC = EF and BC || EF [Given]

⇒ BEFC is a parallelogram. [One pair of opposite sides is parallel and equal]

(iii) BE = CF and BE||BECF [BEFC is parallelogram]

AD = BE and AD||BE [ABED is a parallelogram]

⇒ AD = CF and AD||CF

(iv) ACFD is a parallelogram. [One pair of opposite sides is parallel and equal]

(v) AC = DF [Opposite sides of parallelogram ACFD]

(vi) In ∆ABC and ∆DEF, we have

AB = DE [Given]

BC = EF [Given]

AC = DF [Proved above]

∴ ∆ABC ≅ ∆DEF [SSS axiom]