Irregular Shapes 3: Dynamic Exploration of Polygons and Special Points

This example demonstrates a dynamic geometric figure composed of multiple irregular polygons and their internal special points, highlighting the positional relationships among polygon vertices, edges, and special points such as centroids or incenters. Core mathematical concepts include fundamental properties of polygons, construction and identification of special points (e.g., centroid, orthocenter), and the geometric interpretation of similar triangles and the tangent function on the unit circle. Construction highlights: using GeoGebra's Polygon command to create multiple polygons (poly2, poly3, etc.), defining vertices G, H, I, J and subsequent K, L, M, N, while using text objects (text1, text2) to label key information; auxiliary lines (g, h, i, j, etc.) are constructed to connect special points, forming a complete geometric structure. Suitable for upper secondary or early university students to understand comprehensive properties of polygons and special points, and also useful for teachers creating dynamic geometry lesson materials.