Prior research on students' uses of technology in the context of Euclidean geometry has suggested that it can be used to support students' development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships in hyperbolic geometry. Eight students enrolled in a college geometry course participated in a task-based interview that was focused on examining properties of quadrilaterals in the Poincare disk model. Toulmin's argumentation model was used to analyze the nature of the arguments students provided when they had access to technology while solving the problems. Three themes related to the structure of students' arguments were identified. These involved the explicitness of warrants provided, uses of technology, and types of tasks. (Contains 22 figures, 2 tables and 3 footnotes.)