In this document, I describe and examine some software tools that have been developed to aid in constructions in non-Euclidean geometry. The tools consist of Geometer's Sketchpad scripts that automate hyperbolic "straightedge and compass" constructions in each of three models of hyperbolic geometry. These scripts, based on the earlier work of Alexander and Finzer in the Poincaré disk, automate ten "standard" constructions, including constructing hyperbolic lines and circles in the models, and dropping and raising perpendiculars. The tools can be used to enhance student understanding of hyperbolic geometry in several ways, and I give numerous examples of how they can be effectively used in the classroom.
A grant through the Faculty Development Program at the University of Wisconsin Oshkosh allowed the author to develop the hyperbolic construction tools described in this article. The author greatly appreciates this support. The author also wishes to express his gratitude to the reviewers of this article. Their comments and suggestions have substantially improved the document.