There are two two-dimensional figure with an infinite length. They are rays, and lines.
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A circle is two dimensional because the two dimensions are width and length. 3 dimensional would be width, length and depth but since you can just write it on paper, it has no depth.
An isosceles triangle.
Lines! Yes, they are one-dimensional. Points are zero dimensional, planes are two-dimensional, and prisms and such are three dimensional.
Two dimensional
A square is a two-dimensional figure.