This page shows 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.

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 compass 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 compass width, move the compass to J and draw an arc across the line PQ. Label this point E.	<
4.  Without adjusting the compass width, move the compass 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

Proof

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 lines.

The diagram below is the final drawing above with the green lines added.

Try it yourself

Click here for a printable parallel line construction worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Acknowledgements

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy method)
• Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object