Don't think about lines. Think about polygons. Each part of a shape is defined by the vertices of a polygon. For example, I used 31 vertices to define a part that appears to be a round circle. JMP automatically closes the polygon, so the first vertex is not the same as the last vertex. You leave it open and JMP closes it.
The XY shape file identifies the shape, part, and (x,y) coordinates of these vertices. (Most cases I have seen require only one part per shape.) See the blog post I cited previously for an example you can study.