AAS Congruence Test via Rotation: Angle–Angle–Side on Two Sides

This GeoGebra example demonstrates an angle-based congruence construction using the idea of matching an angle–angle configuration together with a side constraint placed on the corresponding sides of the two angles. It helps verify whether two triangles (or triangle fragments) are congruent by enforcing consistent angle measures and directionality, producing corresponding points that close the construction. Key concepts include triangle congruence criteria (AAS/ASA-style reasoning), angle construction and comparison, and how the relative placement of the side on the two angle rays (same-side/as-positioned constraints) affects the validity of the congruence. The construction uses GeoGebra commands and objects such as Rotate (to align one angle and its adjacent side direction), Angle (to define and track angles α, β, γ), Line (to create the rays/lines forming the triangle sides), Point (to place original and corresponding points like D, E, A, C and their primed images such as A′, D′), and Intersect (to compute the intersection points that determine the final mapped vertices). Suitable for middle/high school geometry instruction, congruence test practice, and students learning construction-based proof techniques through dynamic geometry.