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Abstract: The article analyzes the reasons for the low results shown by school graduates in solving stereometric problems in the UST in mathematics. The authors consider the low level of spatial thinking of the trainees to be one of the main reasons for the failures. In support of this opinion, a test of the spatial thinking of high school graduates in 2018 was conducted. A further comparative analysis of the data obtained with the results of a study carried out in 2005 by one of the authors demonstrated a deterioration in the values of all of its indicators. The article discusses the main factors influencing the formation of spatial thinking of students in the study of the school course of geometry on the example of the section Perpendicularity of lines and planes. A review of school geometry textbooks showed that not adhering to the principle of varying essential features creates prerequisites to the fact that the key concepts of the perpendicular, the projection, the angle between the straight line and the plane will not be formed sufficiently. The experiment conducted with first-year students of the “Pedagogical Education: Mathematics and Computer Science” profile confirmed this point. To solve the identified problems, the authors proposed a series of UST tasks and exercises to formulate the key concepts of stereometry: the projection of a straight line onto a plane, perpendicularity of a straight line and a plane, the angle between a straight line and a plane. In this paper, using the example of the application of the dynamic modeling program Geogebra, it is shown how it is possible to demonstrate the geometrical image of the concepts under consideration at different positions of the image plane. When solving the proposed series of tasks, the geometrical approach is used, while highlighting aspects of the formation of spatial thinking in the part that is associated with operating three-dimensional images: changing its position and structure.