Symmetry of Angles: Exploring Angle Relationships on the Unit Circle

①This example demonstrates the symmetry of angles on the unit circle, showing how angles relate under reflections across the x-axis, y-axis, and origin.②Core mathematical concepts include angle measurement, unit circle, coordinate symmetry, central and inscribed angles, and reflection transformations.③Construction details: Using GeoGebra commands such as Point, Circle, Intersect, Line, and OrthogonalLine, the construction creates the unit circle, intersection points, perpendicular lines, and labeled objects including α, A_1, x_1, c, C, P, a, b, d, y_P, x_P, e, P', P''', P'', f, g, h, i, I, j, k, text1, and text2 to display angle values and symmetric points.④This is suitable for middle and high school students learning angle symmetry, unit circle basics, and introductory trigonometry, as well as for geometry construction demonstrations to visualize how symmetry preserves angle measures.