Euler's Line: Collinearity of Circumcenter, Centroid, and Orthocenter

① This GeoGebra example dynamically demonstrates Euler's line theorem: for any triangle, the circumcenter, centroid, and orthocenter are always collinear. ② Core mathematical concepts include the circumcenter (center of the circumcircle), centroid (intersection of medians), orthocenter (intersection of altitudes), and the property of three-point collinearity, along with fundamental constructions like angle bisectors and perpendicular bisectors. ③ Construction highlights: using GeoGebra commands such as Segment and Polygon to build the triangle; AngularBisector and LineBisector with Intersect to locate the circumcenter; Midpoint and OrthogonalLine to construct the centroid and orthocenter; finally a Line through these three points to visualize their collinearity. ④ Suitable for middle school geometry, competition math, or introductory college geometry courses, this interactive tool helps learners explore the deep relationships among the triangle's notable centers.