SOLVING CONSTRUCTION PROBLEMS IN A TEXTBOOK OF PLANIMETRY BY THE AUXILIARY TRIANGLES METHOD

Abstract

The importance of construction problems is due to the peculiarity of the content of geometry, the leading component of which is constructivism. That is, geometric concepts are defined constructively (the definition is often based on either a drawing, or the construction of a corresponding geometric figure, or consideration of a life situation), proving theorems involves the use of figures, the real existence of which can be confirmed by construction. In the process of solving construction problems, an algorithmic culture is formed as a component of information and communication competence of students, the culture of mental work - the ability to plan their work, perform it rationally, to conduct a retrospective analysis of the problem.
It is substantiated that solving these problems allows to master the educational material more deeply, to strengthen its applied orientation, and, consequently, to effectively form mathematical and other key competencies.
The following sequence of educational material is offered: geometrical place of points, the basic and simplest construction problems, more difficult construction problems of triangles, construction problems of quadrilaterals.
If students master the general methods of finding construction plans, then solving problems to build triangles and quadrilaterals improves.
One of the following methods is recommended - the auxiliary triangle method. The solution to the construction problem can be found by forming an auxiliary triangle in the figure of the desired shape, the method of its construction of which is known, and to find out how to complete this triangle to the desired shape.
Peculiarities of application of this method to solving construction problems are revealed in the article. The development of relevant skills involves the following stages: selection of operations that makes up the content of the method; consolidation and generalization of operations with selected exercises; registration of these operations in the form of instructions. Relevant examples of problems and ways to solve them are given.