Interactive Exploration of Scalene Triangle Congruence and Centroid

①This example demonstrates how to dynamically construct a set of scalene triangles in GeoGebra, using points, vectors, text fields, and sequences to explore triangle congruence and the properties of the centroid (barycenter). ②Core mathematical concepts include congruence criteria for scalene triangles, the geometric meaning of the centroid as the intersection of medians, and the use of natural number sequences to generate multiple points. ③Construction highlights: from the summary, commands such as Point, Vector, Textfield, and Sequence are used, creating multiple vertices (A1-A8, B1-B8) and auxiliary points (C1-C5, D1), with an input box (inputBox1) and variables (x_0, y_zoom) for interactive control, possibly involving scaling and dynamic adjustment. ④This is suitable for middle school geometry or introductory college geometry courses, to visually understand congruence conditions, the relationship between centroid position and triangle shape, and to study patterns via batch-generated points.