Theorems in the school course of mathematics. Methodology of studying theories in the school course of mathematics

When studying algebra and geometry, the teacher and students often come across statements, the truth of which is determined from several positions of the theory by means of proof. In mathematics, they are called theorems. In the school course "theorem" is an already proven statement. However, when getting acquainted with the next theorem, first the teacher, and then the students, prove it again. This is necessary in order to update the previously studied provisions of the theory (in particular the axioms), to facilitate the understanding of the material being studied, to develop in students personal properties that will further help him analyze, compare, predict various situations encountered in the modern world.