Ruler and Compass Construction 22
Line Parallel to a Given Line LM at a Given Distance AB

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1. Arbitrary point C on the line
2. Arcs centered at C, radius AB
3. Arc centered at D, arbitrary radius
4. Arc centered at E, same radius'
5. Ray CF, which is perpendicular to LM
6. Arc centered at C, radius AB
7. Arc centered at D, radius AB
8. Arc centered at G, radius AB
9. Parallel line HG

Why it works:
The construction uses a perpendicular to line LM to create a point G at the given distance from LM.
Then point H completes a square, which has parallel sides.