Question -
Answer -
(i) AB = DE and AB || DE (Given)
Two opposite sides of a quadrilateral are equal and parallel toeach other.
Thus, quadrilateral ABED is a parallelogram
(ii) Again BC = EF and BC || EF.
Thus, quadrilateral BEFC is a parallelogram.
(iii) Since ABED and BEFC are parallelograms.
⇒ AD =BE and BE = CF (Opposite sides of a parallelogram are equal)
, AD = CF.
Also, AD || BE and BE || CF (Opposite sides of a parallelogramare parallel)
, AD || CF
(iv) AD and CF are opposite sides of quadrilateral ACFD whichare equal and parallel to each other. Thus, it is a parallelogram.
(v) Since ACFD is a parallelogram
AC || DF and AC = DF
(vi) In ΔABC and ΔDEF,
AB = DE (Given)
BC = EF (Given)
AC = DF (Opposite sides of a parallelogram)
, ΔABC ≅ ΔDEF[SSS congruency]