Start with a line PQ and a point R off the line.
The goal is to draw a line through R that is parallel to PQ.


1. Mark two points A and B anywhere on the line PQ.
It will be easiest if they are somewhere close to R, but anywhere will actually work.


2. (Optional*). Draw the lines RA and RB to form the triangle RAB.
* This step is optional because the two lines are only there so you can see the triangle and help to understand how the construction works.


3. Mark a point A' anywhere along PQ. 

4. Set compass width to the distance AB. Then, from A',make an arc across the line PQ, creating point B'. 

5. Set compass width to the distance AR.
Then, from A',make an arc above the line.'.


6. Set compass width to the distance BR.
Then, from B',make an arc above the line, creating R' where it crosses the previous arc.


7. (Optional*). Draw the lines R'A' and R'B' to form the triangle R'A'B'.
* This step is optional because the two lines are only there so you can see the triangle and help to understand how the construction works.

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8. Draw a line through points R and R'.
The line R R' is parallel to the line PQ 
