What are the first things that 7th grade students need to get acquainted with, beginning the study of geometry

Abstract

Geometry in school should begin: with a list of the main objects of the discipline, from which individual figures are formed; the main relationships between such objects; well-balanced, clearly formulated axioms. Axioms are the very first statements that are considered purely geometric and are formulated, as a rule, based on the ideas and already considerable experience of the student. Axioms are presented systematically, in the form of non-contradictory, independent statements. In addition, the group of axioms as a whole have to be a complete system, in the formulations of which the basic objects and relations between them, as well as derived figures, are used. The basic objects and the basic relations in which the latter are located are also called basic concepts. We refer to the textbook, which is a classic in the presentation of axiomatics, the textbook of O. V. Pohorelov - a famous, outstanding geometer-theorist and applied scientist of Ukraine. The axiomatics developed by the author is the shortest, and the content component of the development of geometry is much simpler in comparison, for example, with the axiomatics of D. Hilbert.

In the article we emphasize that the main object of the discipline is a figure composed of points, lines and planes, and the most important means of teaching is a drawing. It is also emphasized that geometry as a whole is divided into positional and metric. The role and place of each of these subdivisions are noted. Convincing facts of the applied nature of the subject, its possible application in various fields of science and technology are presented. Brief information about the founder of geometry Euclid and some other historical facts is provided. Further, with colorfully executed drawings and author's comments and adhering to the scheme of O. V. Pohorelov, a system of axioms is given. At the end of the presentation, the concept of a theorem and its proof are presented, an example of a theorem is given, which is also taken from the above-mentioned textbook. In addition, a more detailed concept of an axiom is presented, as well as the definition of something that is often used in geometry.