Constructing a parallel through a point   - Rhombus method

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See also the animated version.

After doing this Your work should look like this
Start with a line segment PQ and a point R off the line.
1.  Place the compasses on point R and set its width to a little more than the distance to the line PQ.
The exact distance is not important.
2.  Draw a wide arc from the right of R around so it crosses the line PQ at two points.
Label the left point J
3.  Without adjusting the compasses' width, move the compasses to J and draw an arc across the line PQ. Label this point E.
4.  Without adjusting the compasses' width, move the compasses to E and draw an arc across the large arc to the right of R. Label this point S.
5.  Draw a straight line through points R and S.
Done. The line RS is parallel to the line PQ

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions