Ruler and Compass Construction 29
Line Halfway Between Parallel Lines

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1. Arbitrary transversal segment AB
2. Midpoint C of AB
(construction 1
3. Arbitrary transversal segment FG
4. Midpoint J of FG
5. Line CJ

Why it works:
Parallel lines cut transversals in equal ratios, and conversely, so joining the midpoints
of any two transversal segments will make a parallel line equidistant from the original lines.