For ten points, identify these shapes whose side lengths obey the Pythagorean Theorem.
The term  cathetus  is an archaic term for certain parts of these objects. Fermat's theorem about these shapes says that their area cannot be a perfect square unless at least one side has irrational length; numbers that can be the area of a rational-sided one of these shapes are called congruent. Polyaboloes consist of special cases of these shapes joined at their edges, and one of these shapes is called primitive if its side lengths are relatively prime. The midpoint of the longest side of one of these shapes is equidistant from all of its   vertices, and if one of these shapes is inscribed in a circle then its longest side is a diameter. For ten points, identify these shapes whose side lengths obey the Pythagorean Theorem.
The term  cathetus  is an archaic term for certain parts of these objects.
right triangles [prompt on triangles]