Geometry Construction Reference

This guide was originally written for my own geometry students. These instructions can be found in most elementary geometry books, but it might be more convenient to have them all in one place, rather than scattered throughout the book.

Compass and straightedge construction can be far more complex, but I have no intention of adding to this work. These are the basics. Use them as tools to build an understanding of higher concepts.

What is construction? Follow this link to learn the rules. Construction is not simply drawing.

About the instruments. If you are not familiar with the drawing instruments, this link has a few tips that might be helpful.

Word Version – If you plan on printing this guide, the graphics and the formatting will look better in the original format, which is Word. Download the Word document here: conrefw.docx

Construction 1	Construct the perpendicular bisector of a line segment, or construct the midpoint of a line segment.
Construction 2	Given a point on a line, construct a perpendicular line through the given point.
Construction 3	Given a point not on the line, construct a perpendicular line through the given point.
Construction 4	Construct the bisector of an angle.
Construction 5	Construct an angle congruent to a given angle.
Construction 6	Construct a line through a given point, parallel to a given line.
Construction 7	Construct an equilateral triangle, or construct a 60 angle.
Construction 8	Divide a line segment into n congruent line segments.
Construction 9	Construct a line through a given point, tangent to a given circle.
Construction 10	Construct the center point of a given circle.
Construction 11	Construct a circle through three given points, or circumscribe a circle about a given triangle.
Construction 12	Inscribe a circle in a given triangle.

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Last update: June 17, 2026 ... Paul Kunkel whistling@whistleralley.com
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