Taxi Geometry and Euclidean Geometry: Congruence and Similarity of Triangles

Authors

• Jose Carlos Pinto Leivas, Universidade Franciscana, Santa Maria, Brazil
• Osvaldo Jesus Rojas Velazquez, Facultad de Educacion, Universidad Antonio Narino, Colombia
• Diana Carolina Perez Duarte, Facultad de Educacion, Universidad Antonio Narino, Colombia
• Randy Zabaleta Mesino, Fundacion Universitaria Tecnologico Comfenalco, Colombia

Abstract

This article presents an instrument that describes the experience implemented with students of a graduate programme in the courses of Analytic Geometry and Linear Algebra. The purpose of the instrument, as a didactic resource, was to analyse how the connections between the classical cases of congruence and similarity of triangles in Euclidean Geometry and in Taxi Geometry can be explored. The metric analysis of the productions shows that the three classical congruence criteria - SSS, SAS and ASA - cease to hold under the taxicab metric, and that equilaterality does not imply equiangularity in that geometry. In addition, a neutrosophic logic framework is applied in order to assess the degree of certainty, indeterminacy and contradiction of each category of bibliographic evidence on which the proposal rests.

Recommended Citation

Pinto Leivas, Jose Carlos; Osvaldo Jesus Rojas Velazquez; Diana Carolina Perez Duarte; and Randy Zabaleta Mesino. "Taxi Geometry and Euclidean Geometry: Congruence and Similarity of Triangles." Neutrosophic Sets and Systems 101, 1 (2026). https://digitalrepository.unm.edu/nss_journal/vol101/iss1/6