Teaching geometry faces such problems as a lack of qualified teachers, the lack of modern methods and materials for teaching geometry. To solve these problems, it is necessary to improve the training of mathematics teachers even within the walls of the pedagogical university. This article discusses the basic skills of solving geometric tasks, which play an important role not only in teaching mathematics, but also in general development. We want to draw attention to how the correct design of solutions and proofs of geometry tasks can help students develop analytical, logical and critical thinking. It requires precision, consistency and clarity in the expression of thoughts. In the course of the study, students were involved – future teachers of mathematics, to the solutions of geometric tasks of which strict design requirements were imposed. As a result, students learned how to correctly formalize solutions and proofs of geometric tasks, which served as a good help for the development of their skills in future professional activities, skills of analysis, logical and critical thinking, as well as the development of communication skills and teamwork abilities