Open Middle Triangle Angle Sum Problem (V2): Constructing and Checking Interior

This GeoGebra example uses an “Open Middle” setup to guide learners toward discovering and verifying the interior angle sum of a triangle through interactive construction and measurement. It centers on how angle relationships emerge when auxiliary rays, segments, intersections, and rotated copies of geometry are introduced. Key concepts include triangle interior angles, angle construction and measurement (Angle), intersection-based construction (Intersect), and rotation-based correspondence of angles (Rotate). Construction highlights: Intersect and Point establish key vertices and intersection points; Ray and Segment build the triangle edges and supporting lines; Polygon forms the triangle; Rotate generates matching geometric configurations to reveal angle equivalences; Angle produces the measurable/annotated interior angles (e.g., α and related marked angles); If controls case-based behavior and display; Distance and Length support measuring relevant quantities. The scene includes the triangle (A, B, C), auxiliary points (such as B′/A′-type points), angle objects, and text labels. Suitable for secondary school geometry exploration, open-ended problem discussions, and introductory proof-by-construction practice.