Abstract
The main content of the article is devoted to the geometric problems of mathematical school olympiads. The study revealed the types of operating with spatial images in the process of solving problems, the stages of forming spatial representations of students in the study of geometry and objectives of the course of visual geometry. It was concluded that the formation of spatial, topological, spatial, projective representations goes through successive stages, developing the geometric skills of schoolchildren. Olympiad tasks, designed on the basis of school programs and textbooks on geometry, make it possible to check the formation of the geometric skills of schoolchildren. The article may be of interest to mathematics teachers, students and schoolchildren who are interested in methods of solving olympiad problems in geometry.
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