A document analysis on triangle congruence and similarity

Congruence and similarity in triangles constitute one of the fundamental components of geometry, which is a branch of mathematics. The purpose of this study is to investigate scientific research and mathematics textbooks with respect to the terminology employed for the criteria of congruence and similarity in triangles. In addition, this study aims to analyze the structure of the aforementioned terminology across various types of documents, its consistency with the axiomatic structure, and the internal coherence of the terms within these documents. Accordingly, eight mathematics textbooks from both national and international sources, twenty-eight academic articles, eight conference proceedings, fourteen graduate theses, and seven university-level reference books were examined employing document analysis; the data obtained were subsequently analyzed through content analysis. As a result of the analyses, it was determined that in the documents constituting the scope of the study, the terminology related to the criteria of congruence and similarity was not presented in a common and consistent manner, the alignment with the axiomatic structure was mostly not achieved, and different terms were used for the same concepts. Notably, considering the influential role of mathematics textbooks in the teaching process, it is a striking finding that no common standard has been established for the terminology related to the criteria of congruence and similarity in mathematics textbooks used in Turkey, the United States, South Korea, and the United Kingdom. In this context, it is emphasized that the use of a common, clear, and consistent terminology by mathematics textbook authors and curriculum developers would enhance students' understanding and strengthen mathematical thinking. Accordingly, several recommendations have been put forward for the relevant stakeholders to ensure terminological consistency, specifically in relation to congruence and similarity in triangles, and to avoid neglecting the axiomatic structure of mathematics.