A Proof Without Words via Geometric Construction: Circles, Rotation, and Angle R

This example demonstrates a “proof without words” by using a constructed geometric diagram to make a mathematical claim visually inevitable. The main visual phenomenon comes from constraints created by circles and sector geometry, where rotation and angle measurement reveal a necessary correspondence (e.g., equal or corresponding angles under a transformation). It highlights key concepts such as geometric construction, circle geometry with intersection points, rotation as a transformation, and explicit angle labeling/measurement. Construction-wise, the GeoGebra setup is built from commands listed in the construct summary: Point, Circle, Intersect to create base points and circle intersection points; Rotate to generate rotated (transformed) configurations; Segment and Angle to define and display segment connections and the measured/marked angle relationships; Sector and Polygon to form sector regions and polygonal frameworks that support the layout of the argument; CurveCartesian to include a curve for additional structure or reading of the relation; and Sequence, Join to organize repeated or connected elements during the construction. Suitable for upper secondary through early university geometry courses and for teaching/learning transformation-based reasoning and proof visualization.