Step-by-step Instructions

After doing this	Your work should look like this
Start with a line segment PQ and a point R off the line.
1.  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.
2.  With the compass width set to about half the distance between R and J, place the point on J, and draw an arc across both lines.
3.  Without adjusting the compass width, move the compass to R and draw a similar arc to the one in step 2.
4.  Set compass width to the distance where the lower arc crosses the two lines.
5.  Move the compass to where the upper arc crosses the transverse line and draw an arc across the upper arc, forming point S.
6.  Draw a straight line through points R and S.
Done. The line RS is parallel to the line PQ

This construction works by using the fact that a transverse line drawn across two parallel lines creates pairs of equal corresponding angles. It uses this in reverse: by creating two equal corresponding angles, it can create the parallel lines.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• 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

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

Non-Euclidean constructions

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