Construction of a Parallel Line


1. Start with a line PQ and a point R off the line.

Geometry construction with compass and straightedge or ruler or ruler

2. Draw a transverse line through R and across the line PQ at an angle, forming the point J where it intersects the line PQ. The exact angle is not important.

Geometry construction with compass and straightedge or ruler or ruler

3. With the compasses' width set to about half the distance between R and J, place the point on J, and draw an arc across both lines.

Geometry construction with compass and straightedge or ruler or ruler

4. Without adjusting the compasses' width, move the compasses to R and draw a similar arc to the one in step 2.

Geometry construction with compass and straightedge or ruler or ruler

5. Set compasses' width to the distance where the lower arc crosses the two lines.

Geometry construction with compass and straightedge or ruler or ruler

6. Move the compasses to where the upper arc crosses the transverse line and draw an arc across the upper arc, forming point S.

Geometry construction with compass and straightedge or ruler or ruler

7. Draw a straight line through points R and S.

Geometry construction with compass and straightedge or ruler or ruler

8. The line RS is parallel to the line PQ

Geometry construction with compass and straightedge or ruler or ruler