A square, a rectangle and a rhombus are three examples.
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A square is a 2 dimensional shape, but it can be divided into 2 or more triangles, or more smaller squares, or hexagons and triangles, or octagons and triangles, or really any rectilinear figure and triangles. If you mean what two dimensional shapes can compromise the surface of a cube, or rectangular prism, then you want squares. if you mean what 1 dimensional figures can make the perimeter of a square, then you want lines (straight lines).
Well, parallel lines are a pair of lines that could go on forever without intersecting. They could be going in the vertical direction or in the horizontal direction. I'm going to list a few shapes; circle triangle I'm sure there are more, but those are the only ones I could think of at the top of my head.
Infinitely many. Polygons with 6 or more sides can have 3 pairs of parallel lines. Polygons with 7 or more sides can have a set of three parallel lines.
Hexagon
A square