Parallel Line

1. Begin with a line and a point P not on that line.

2. Construct an arbitrary point A on that line.

3. Construct the line $$\overset{\longleftrightarrow}{A P}$$

4. Construct the circle $$\overset{\frown}{A P}$$. It intersects the first line at point B.

5. Construct the circle $$\overset{\frown}{P A}$$. It intersects the second line at point C.

6. Copy the distance from point P to point B. Construct a circle of that radius centered on C. It intersects circle $$\overset{\frown}{P A}$$ at point D.

7. The line $$\overset{\longleftrightarrow}{P D}$$ is parallel to the first line. Also, the angle $$\angle{P A B} = \angle{C P D}$$.