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