Dynamics of Triangle Similarity: Exploring Similitude Ratios through Interactive Sliding Controls

Abstract

Similarity is crucial in mathematics and other fields. It relates to different curricular mathematics content, for instance, proportionality, measures, and shapes. This article discusses the interactions of prospective teachers when performing similarity tasks in a multiuser, online, virtual, and synchronous environment with Geo Gebra, the VMTwG. The analyzed task focused on the similarity ratio from a slider. The focus here is to illustrate how the subjects interact when dragging free points of two triangles created with dependence on each other and using a checkered mesh. Data production came from registers written and Geo Gebra screen construction by participants and VMT replayer. The use of the slider may represent a more potent form of thought process, which implies both the global observation of geometric properties, the validation of conjectures and checking detailed results.