In figure, AB ∥ DE, AB = DE, AC ∥ DF and AC = DF. Then, BC ∥ EF and BC = ___ .
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 …..(i)
Now, in quadrilateral ACFD,
AC ∥FD and AC = FD
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 [from Eq. (iii)]
So, BCFE Is a parallelogram,
∴ BC = EF and BC ∥ EF
Hence proved.