Points in Triangle: Centroid Construction

This example demonstrates the construction of specific points (such as the centroid) inside a triangle using geometric tools like angle bisectors and perpendicular bisectors. The core mathematical concepts include the centroid (barycenter) of a triangle, angle bisectors, perpendicular bisectors, and the relationship between polygon areas and points. Construction details: Using GeoGebra commands Polygon to create triangle ABC, AngularBisector to construct angle bisectors, LineBisector for perpendicular bisectors, and Intersect to find intersection points D, E, F, then connecting these to form inner polygon poly1, with auxiliary lines f_1, d_1, e_1 to further determine points G and H. Suitable for middle and high school geometry lessons, helping students understand the geometric construction and properties of special points in triangles, and explore how the centroid divides the triangle into equal-area regions.