AAA Triangle Congruence Investigation: Angle–Angle–Angle

This example demonstrates how to investigate triangle correspondence and congruence-like behavior under the Angle–Angle–Angle (AAA) condition by matching key angles and comparing the resulting configurations. It centers on geometric reasoning about triangle congruence (and what AAA does or does not guarantee), angle construction and measurement, and how rigid transformations affect vertex alignment. Construction strategy in GeoGebra: build sides with Segment, apply Rotate to move/align one triangle by rotating around a chosen vertex, define and measure critical angles using Angle together with Ray for the involved rays, and compute necessary intersection points with Intersect to obtain corresponding vertices/points and related segments (e.g., the primary triangle and its rotated/constructed counterpart, along with angle labels such as α, β, γ and α', β', γ'). The result helps learners visually test hypotheses using dynamic geometry. Suitable for middle/high school geometry classes, exploratory learning, and competition-style concept checks.