Constructing Parallel Line through a Point - Rhombus Method
Constructing Parallel Line using Rhombus
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How to construct a line parallel to a given line through a given point with compass and straightedge or ruler. This construction works by creating a rhombus. Since we know that the opposite sides of a rhombus are parallel, then we have created the desired parallel line. This construction is easier than the traditional angle copy method since it is done with just a single compass setting.
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