Publication at Faculty of Mathematics and Physics |
2015
Abstract
Dynamic geometry systems allows students to explore new constructions, but new constructions usually need a proof of its correctness. The paper brings a lot of examples of construction of a point which divides a given segment at a ratio of 1 : (k MINUS SIGN 1), for positive integer k < 20.
Presented constructions can serve as task resource for practicing proofs in plane geometry. Proofs of the correctness of those constructions need knowledge of elementary geometry rules and theorems, especially the similarity of triangles and the power of a point to a circle theorem.