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A quadrilateral is a parallelogram if it...

A quadrilateral is a parallelogram if its opposite sides are equal.

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`AC` is a transversal and also `AB` parallel `CD`.
`therefore /_BAC=/_DCA` (Alternate angles)
In `/_\ADC` and `/_\CBA`, we have
`AB=CD` (Given)
`/_BAC=/_DCA` (Alternate angles)
`AC=CA` (Common)
`/_\ADC~=/_\CBA` by the `SAS` rule.
Hence, by `CPCT`,
`DA=BC` and `DC=AB`
Thus, a pair of opposite side is parallel and congruent in quadrilateral `ABCD`.
`therefore ABCD` is a parallelogram.
Hence proved.
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