Exploring Properties of Quadrilaterals in the Poincaré Disk Model of Hyperbolic Geometry Using the Dynamic Geometry Software

Abstract

The purpose of this study was to have preservice mathematics teachers explore important properties of hyperbolic quadrilaterals in the Poincaré disk model using the Dynamic Geometry Software (DGS). The participants comprised 40 preservice mathematics teachers at Rajabhat Rajanagarindra University, Thailand, who had enrolled in the Foundations of Geometry course at the second semester of the academic year 2015. The instruments were activity packages exploring properties of hyperbolic quadrilaterals using DGS. The results indicated that preservice mathematics teachers could make conjectures and verify properties of hyperbolic quadrilaterals correctly and rapidly. The use of DGS can help students visualize this abstract geometry.