DEVELOPMENT OF STUDENTS' RESEARCH COMPETENCE BY TEACHING THE EULER LINE AND EULER CIRCLE

Today, the rapid development of society requires from the educational system not only the upbringing of specialists with academic training, but also individuals who are open to new ideas, capable of exploring complex problems, and thinking creatively and critically. The rapid growth of science and technology, the increase in information flows, and the integration of new technologies into our daily lives make it imperative that the student is not limited to being a mere recipient of ready-made information. On the contrary, the student must form as an individual capable of applying the acquired knowledge in practice, conducting analysis, forecasting, solving difficult problems, and drawing independent conclusions. Mathematical experiments and research play an important role in the mathematical preparation of students. It has been proven that their use increases efficiency in achieving a deeper and more complete assimilation of mathematical knowledge, forming in students qualities of creative thinking, skills of formulating hypotheses, conducting logical analysis, generalizing, and summarizing results. Therefore, the purpose of the article is to teach a geometry topic by organizing research while having students conduct mathematical experiments in the GeoGebra computer environment. The article considers a didactic development proposed for teaching the topic "The Euler Line and the Euler Circle" in classes with an in-depth study of geometry. In order for students to understand these two theorems to a degree that allows their application, they must prove them independently. Since the properties of many points are considered simultaneously here, to ensure independent mastery by students, complex theorems were divided into tasks (lemmas) while maintaining their sequence. In this methodical development, the teacher acts only as a guide, while the student takes on the role of a researcher of the properties of these remarkable points. It is recommended to use this system for 9th-grade students in elective classes, specialized classes, and Olympiad preparation sessions.