AAA Triangle Congruence Exploration: Does Angle-Angle-Angle Guarantee Congruence

This interactive GeoGebra example demonstrates whether two triangles with three pairs of equal angles (AAA condition) are necessarily congruent. The core mathematical concept is triangle congruence criteria, specifically that AAA does not prove congruence but only similarity. Construction details: using GeoGebra commands such as Segment, Rotate, Angle, Ray, and Intersect, two triangles are built with adjustable angles α and β. By dragging vertices or using sliders, students can observe that while the angles remain fixed, the side lengths change, showing that AAA produces similar but not congruent triangles. This exploration is ideal for middle or high school geometry classes to help students distinguish between congruence and similarity, and to understand why AAA is not a valid congruence theorem while SSS, SAS, and ASA are. The dynamic nature of the applet encourages inquiry-based learning and visual proof.