It's not clear at all what you mean by "normal shaped".
For that matter, it's not clear what you mean by "same".
So I'll have to answer in a somewhat abnormal way:
IF you could cut out one of the figures, and by moving it
or rotating it BUT NOT turning it over to see the other side
of the paper, you could exactly lay it on top of the other one
and it would exactly fit, then the two figures are congruent.
I think that's what you're describing, but I can't be sure.
