Although it is impossible to construct a parallel to a line AB with only a straightedge, you can construct a parallel to a given line AB if there is a line segment (AB) on the line that is bisected by a point C.

If you are trying to draw a parallel through a specific point, make this point G or F. Draw a ray through G or F and put a point D on the ray starting from point A or B. Take the other point (A or B) and draw the other ray through D. Draw AG and call the intersection of DC and AG "E". Draw a ray BE. Where ray BE intersects DA put a point F (or G). Connect F and G with line FG. FG is parallel to AB.

If you are constructing a parallel through any point, draw rays AD and BD where D is any point. Draw DC (C is the midpoint of AB). Draw AG and call the intersection of DC and AG "E". Where it intersects DB, put a point G. Draw a ray BE. Where ray BE intersects DA put a point F. Connect F and G with line FG. FG is parallel to AB.

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