Possibility of the use of Cartesian method in the proofs of fundamental theorems of school planimetry

TL;DR

This paper explores how the Cartesian coordinate method can be effectively used to prove fundamental school-level planimetric theorems, offering a new perspective on teaching geometry.

Contribution

It demonstrates the application of Cartesian coordinates in proving key geometric theorems, proposing a new approach for geometry education.

Findings

Cartesian method simplifies proofs of basic geometric theorems

Provides a structured plan for teaching geometry using Cartesian coordinates

Highlights the central role of Cartesian method in school geometry

Abstract

We show how Cartesian method can be used in the proof of fundamental planimetric topics of the school course, such as introduction of trigonometric functions, equation of a line and similarity of triangles. This work also can be considered as a plan of the school course of geometry, where the Cartesian method plays the main role.