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Answers
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]