How to...construct a parallel line to a given line through a point off of the line segment

This construction combines all of the constructions you have learned to construct parallel lines.
There are many ways to construct parallel lines, however this is my favourite and easiest way to do it.

Step 1
Extend a ray from one of the endpoints on you line segment to make an acute angle. Make sure that the ray intersects the given point.





Step 2
Make an arc from the starting point to the given point. Keep this measure. Using this measure, measure from the given point(which is on the ray) and make an arc. Make a point where the arc intersects the ray. Label this point.






Step 3
Measure from the given point to where the first arc that you made intersects the given line segment. Using this measure, go from the last point you just made and make an arc. Make a point where the arc you just made intersects the other arc. Label this point.



Step 4
Connect the point that you just made to the original given point. Label the line.

It doesn't look like the lines are parallel in the picture, but that is only because the surface i was taking the picture on was not flat. That is why it appears to bulge and then get smaller in the bottom left hand corner.