
How to construct a line parallel to a given line, passing through a given point?

1. 
 Start with two lines forming an (acute) angle, one of which (the upgoing line) defines the given line. The other one is an auxiliary line.


2. 
 On the auxiliary line, determine the given point. (The auxiliary line must pass through the given point).


3. 
 Construct an arc with its center at the angular point, and with a suitable radius. It must intersect with both lines.


4. 
 Construct an arc with the same radius and orientation as arc 3, with its center at point 2.


5. 
 Construct an arc with its center at the intersection of arc 3 and the auxiliary line, passing through the intersection of arc 3 and the upgoing line.


6. 
 Construct an arc with the same radius and orientation as arc 5, with its center at the intersection of arc 4 and the auxiliary line.


7. 
 Draw a line through point 2 and the intersection of arcs 4 and 6, and extend it where necessary.


8. 
 Line 7 is the line to be constructed. It runs parallel to the given line, and passes through the given point.

