§1. Point, line, plane

A Grade 7 topic in Geometry: “§1. Point, line, plane” (pp. 5–9, I. B. Bekboev, A. A. Borubaev, A. A. Ayylchiev). In geometry some concepts have to be accepted without a definition. Point, line, plane and set are taken as such primary, basic concepts; they are called the basic, or first, concepts. All other concepts are defined only through these basic ones. Points are marked on a drawing with the tip of a pencil and denoted by capital Latin letters (A, B, C …), while lines may be denoted by small Latin letters (a, b, c …). A line can be extended without end, and a drawing shows only parts of it. A plane also extends without end in every direction. The notation M ∈ a means that the point M belongs to the line a, while B ∉ a means that the point B does not belong to the line a. The basic properties (axioms) are stated as follows: I₁ — for any line there are points lying on it and points not lying on it; I₂ — through any two points passes exactly one line.