Angles as Rotations: Dynamic Visualization

① This example demonstrates how an angle can be interpreted as a rotation, showing a ray rotating around a vertex to form an angle and the resulting positions of rotated segments. ② The core mathematical concept is the rotational definition of angles, including rotation center, rotation angle, direction (positive/negative), and the relationship between the original and rotated figures. ③ Construction details: Using GeoGebra commands Segment to create lines, Rotate to rotate a segment around point A by a specified angle, and Angle to mark the rotated angles β₁ and γ; objects include B, A, a, A', C, a', E, D, b, D', F, b', with text objects text1 and text2 displaying angle measures. ④ Suitable for middle and high school students learning geometric transformations and angle concepts, as well as teachers for classroom demonstrations to visualize how angles arise from rotation, laying groundwork for trigonometry and vector rotations.