The collinearity of barycenters related to a polygon

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

Information: The collinearity of barycenters related to a polygon