Google Classroom
GeoGebraGeoGebra Classroom

The collinearity of barycenters related to a polygon

ARTICLE ACTIVITIES

These activities include the files that support and illustrate the development of the article: "A proposal to explore geometry with GeoGebra: Graphical exploration and formal demonstration of the Collinearity of the barycenters of a polygon" of the teachers: Saulo Mosquera, Walter Castro and Marlio Paredes. This article generalizes a geometric property observed in a triangle by Bonelo-Ayala et al (2024) which is: Consider a triangle  ABC, any straight line and let A’, B’, C’ be the reflections of the points A, B, C on the straight line then the barycenters of the triangles ABC, A’BC, AB’C and ABC’ are collinear and the line of collinearity is perpendicular to the straight line".

The collinearity of the barycenters in a triangle.

The collinearity of the barycenters in a quadrilateral

Illustration for testing collinearity in a triangle.

The algebraic definition of centroid for a triangle, quadrilateral and pentagon

The collinearity of the barycenters in a pentagon

The concurrence of the pentamedians

The geometric definition of the barycenter of a pentagon.

Arithmetic and geometric experiments in a pentagon.

The proof of the collinearity of baricenters in a pentagon