Click here for a printable segment copying worksheet

This demonstration shows how to make a copy of a line segment using only a compass and straight edge. See "Introduction to Euclidean Constructions" We start with a line segment

PQ

. The result is another line segment

RS

congruent to the first.

Note that the straightedge can be a ruler, but it is not used to actually measure anything, just to draw straight lines. Ignore the markings on it.

Step 1	Mark a point R that will be one endpoint of the new line segment.
Step 2	Set the compass point on the point P of the line segment to be copied.
Step 3	Adjust the compass width to the point Q. The compass width is now equal to the length of the line segment PQ.
Step 4	Without changing the compass width, place the compass point on the the point R on the line you drew in step 1
Step 5	Without changing the compass width, Draw an arc roughly where the other endpoint will be.
Step 6	Pick a point S on the arc that will be the other endpoint of the new line segment.
Step 7	Draw a line from R to S.
Step 8	Done. The line segment RS is equal in length (congruent to) the line segment PQ .

Other constructions

Lines

• Introduction to constructions
• 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

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