PROBLEMS OF CONSTRUCTION OF PARTS OF ONE TYPE OF POLYHEDRONS - Musayelyan, R. (SUSh Scientific Proceedings, 2025)
The work deals with one of the most difficult topics of school geometry - segment construction. In the school curriculum, students are usually presented with tasks where the three points in question, through which the segment passes, have a special location. Of these three points, at least two must belong to different sides of the multifaceted. Such tasks are easily solved and are more understandable to children, than the points through which the desired segments pass can be located on the polyhedron in different ways, creating, indeed, more difficulties. In each of the cases considered in this work, at least two of the three points through which the searchable components must pass are interior points of the different sessions of the considered multifaceted. An internal point should be understood as a point belonging to a session, but not on a side. Note that there are many options for the arrangement of three points on the same polyhedron. Naturally, one of them, the most general case, is considered in the work. The polygons considered in the work are triangular, tetragonal, pentagonal pyramids, as well as prisms of the same name. Illustrative drawings are made accordingly.