1.) Begin with an arbitrary line segment.
2.) Construct two lines perpendicular to this segment which go through each of the endpoints.
3.) Construct a circle which has its center as one of the endpoints of the original segment and its radius length as the length of the segment. Mark the point where the circle intersects one of the perpendicular lines.
4.) Construct a line parallel to the original segment which passes through the intersection point found in the previous step.
5.) Construct segments as sides of square. Hide extra constructions.
Click here to see the construction in GSP