A quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.

Explanation

Given: `ABCD` is quadrilateral and `AB` parallel `CD`, `AB=CD`.
To prove: `ABCD` is a parallelogram.
Proof: `AC` is a transversal and also `AB` parallel `CD`.
`therefore /_BAC=/_DCA` (Alternate angles)
In `/_\ADC` and `/_\CBA`,
`AB=CD` (Given)
`/_BAC=/_DCA` (Alternate angles)
`AC=CA` (Common)
`:./_\ADC~=/_\CBA` [By the `SAS` rule]
`DA=BC` [By `CPCT`]
Thus, both the pair of opposite sides are equal in the quadrilateral `ABCD`.
`therefore ABCD` is a parallelogram.
Hence proved.