Geometry is a problematic area in the teaching of mathematics at all levels of education in Slovakia and abroad. In Slovakia, this trend is indicated by the results of national test at the end of the second level of primary schools (Testovanie 9), which is designed for pupils in 9th grade. Based on various researches and also on our experience, pupils often have difficulties in solving various geometric problems related to triangles, despite the amount of time they devote to this topic. The aim of our research was to qualitatively analyze and evaluate pupils' solutions to geometric problems focusing on triangles and their properties and also to identify pupils' misconceptions when solving the problems. These tasks were one part of the geometry test designed according to the three levels of mathematical competence defined in the OECD PISA study (reproduction, connection and reasoning), and are based on the tasks in Testovanie 9. The research sample consisted of 760 ninth-grade pupils and was carried out in 29 primary schools located in 23 cities in Slovakia. The results of our research correspond with other studies that have examined the topic of triangles at the second level of primary education. Based on these findings, it is clear that the topic of triangles is still relevant. Pupils often do not see the connections between the acquired knowledge and have only formal knowledge of geometry. It is also important for teachers to know how their pupils think when solving geometry problems, which can help them to gauge pupils' reasoning abilities and also prompt teachers to rethink the procedures used in the teaching process. Further details of our findings and their causes are presented in the paper.

Keywords: Geometry education, triangle, problem solving, nine-grade pupils.