Given:
AB||DE,AB=DE,AC||DF and AC=DF
To prove: BC||EF and BC=EF
Proof: AC||DF [Given]
And AC=DF [Given]
∴ACFD is a parallelogram.
AD||CF.......(1) (∵ opposite side of a || gm are parallel)
and AD=CF.......(2) (∵ opposite side of a || gm are parallel)
Now, AB||DE [Given]
and AB=DE [Given]
∴ABED is a parallelogram.
AD||BE.......(3) (∵ opposite side of a || gm are parallel)
and AD=BE.........(4) (∵ opposite side of a || gm are parallel)
From (1) and (3), we get,
CF||BE
From (2) and (4), we get,
CF=BE
∴BCFE is a parallelogram.
⇒BC||EF (∵ opposite side of a || gm are parallel)
and BC=EF (∵ opposite side of a || gm are
hence proved.
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