Abstract

BONELO-AYALA, Yonathan; BENITEZ-MOJICA, David  and  MUNOZ-POSSO, Jhovanny. A New Geometric Theorem and its Application in Conjecture Construction through a Dynamic Geometry Environment. Rev. Cient. [online]. 2024, n.49, pp.44-61.  Epub June 19, 2024. ISSN 0124-2253.  https://doi.org/10.14483/23448350.20680.

This article presents a new result in Euclidean geometry involving the centroids of a triangle and the triangles formed by modifying one vertex of the preceding one through its axial reflection with respect to a given line. These centroids are collinear, and the line containing them is perpendicular to the initial one considered for the axial reflections. Additionally, a generalization of the aforementioned theorem for quadrilaterals is provided, and the formal proofs of both results are detailed. This is presented following the steps for the construction of conjectures by Benítez Mojica and Santos-Trigo, using dynamic geometry environments that can be employed in future experiences in Euclidean geometry courses with the aid of new technologies.

Keywords : conjecture; drag; dynamic geometry environment; teaching geometry.

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