[Math] ny theorem about figures of equal area and perimeter being congruent

alternative-proofgeometry

I had an idea, that all geometric objects, that are different, as they're not a translation, rotation, and a reflection of one another cannot have the same area AND perimeter, as compared to ONE ANOTHER. They can't be CONGRUENT.

If the shapes are similar there is no similar shapes can contradict this "idea", or that is what I think.

I know that there was some idea on this, is there any theorem, or specific idea, which this is expressed?

Best Answer

Counter-example without words (except for these):

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