Question

In the following figure, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

Answer 1

Given: In the following 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

Now, in quadrilateral ACFD, AC || FD and AC = FD  ...(i)

Thus, ACFD is a parallelogram.

AD || CF and AD = CF  ...(ii)

From equations (i) and (ii),

AD = BE = CF and CF || BE  ...(iii)

Now, in quadrilateral BCFE, BE = CF

And BE || CF  ...[From equation (iii)]

So, BCFE is a parallelogram.

BC = EF and BC || EF.

Hence proved.