Rotation of an Equilateral Triangle

This GeoGebra example demonstrates the geometric rotation of an equilateral triangle about a given point. Using the Segment and Polygon commands, four equilateral triangles are constructed step by step with vertices labeled A through E, illustrating the positional relationships and corresponding side-angle properties before and after rotation. Leveraging the principle that complex number multiplication can achieve planar rotation, the construction intuitively presents the invariance of an equilateral triangle under rotational transformation, such as constant side lengths and internal angles. This applet is suitable for learning plane geometric transformations, the connection between complex numbers and geometry, and the symmetry properties of regular polygons.