Question

Question 11 (v)
In $\Delta ABCand\Delta DEF$ ,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 AC = DF .

Answer 1

It can be observed that ABED is a parallelogram (AB =DE, AB||DE) and BEFC is also a parallelogram (BC = EF, BC||EF)

Therefore,
AD=BE and AD || BE
(Opposite sides of a parallelogram are equal and parallel)

And, BE=CF and BE || CF
(Opposite sides of a parallelogram are equal and parallel)
AD = CF and BE || CF

As we have observed that one pair of opposite sides (AD and CF) of quadrilateral ACFD are equal and parallel to each other, therefore, it is a parallelogram.

As ACFD is a parallelogram, therefore, the pair of opposite sides will be equal and parallel to each other.

$\therefore AC\parallel DFandAC=DF$