To construct a parallel to a line through a point not on the line using paper folding, you can perform the construction twice

The correct answer is:

The midpoint of a segment.

Explanation:

To construct a line parallel to another line through a given point, the first thing you do is fold the given line onto itself, making sure that the given point is on the fold. This is the same construction used to find the midpoint of a segment.

Unfold the paper, and the crease made with the fold creates a line through the given point and given line. Fold this new line (crease) onto itself, making sure the given point is in the fold. This is again the same construction used to find the midpoint of a segment, and this creates our parallel line through our given point.