The issue under study is urgent today because there is a necessity for students to develop skills in working with the mathematical problem at the final stage of its solution in order to get excellent results while learning geometry and when encouraging intellectual and personal development. The aim of the research is to develop the theory and methodology of the final stage of working with planimetric problems as a means of improving the quality of geometry knowledge of schoolchildren. The key research method of the issue is match making between the components of the final stage of working with the mathematical problem and their corresponding operations. The research has resulted in defining the structure of the final stage of working with mathematical problems. It allowed to perform a certain set of operations composing the skill of working with the mathematical problem at the final stage of its solution. The article shows the technique for composing special tasks in order to form operations corresponding to the final stage of working with mathematical problems. It is proved that students’ ability to carry out the above described stage of solving a mathematical problem helps them to get excellent results while learning geometry. The author’s technique of teaching students to work with the mathematical problem at the final stage of its solution, proposed in the article, can be used by mathematical teachers in their practical work, by the authors of resource books for students and teachers and by students of pedagogical universities while doing their special courses.