ofcurse I know that all the rectangle are parallelogram.
but you can't proof that it is rectangle with out proof it is parallelogram usually...
Anyway, you said both of them can be parallelogram but one of them isn't.
and we don't need to proof here that someone is a parallelogram, we need to proof that some isn't parallelogram.
The issue is that there are multiple representations of quadrilaterals, both parallelograms or not, with one pair of opposite sides being x and a diagonal being y. These constructions you have shown us make it impossible to definitely determine whether or not they're parallelograms, since there are possibilities for both depending on the values of the ambiguities. What I'm led to believe is that you or the teacher left out some angle measures or side lengths or parallel notches.