Triangle Congruence Theorems: Construction and Verification

This GeoGebra example constructs two triangles and visually verifies congruence by comparing the key measurable features—side lengths and interior angles—under geometric transformation. It demonstrates the decision logic behind triangle congruence theorems and shows how the corresponding elements match when the triangles are congruent. The main concepts include triangle congruence, correspondence of vertices, interior angle computation, and distance (side-length) measurement, together with transformation-based exploration (e.g., dilation to generate related configurations for comparison). Construction highlights: Polygon is used to build the original triangles (A, B, C and D, E, F) and their polygonal counterparts; Dilate generates a scaled copy (e.g., A2, B2, C2 with associated parameters like t1 and t2) to study how changing configuration affects measurable quantities; InteriorAngles produces the angle sets (α, β, γ and i/δ/ε/ζ-style angle objects) for direct comparison; Distance computes side lengths (distanceAB, distanceBC, distanceAC, and distanceDE, distanceEF, distanceDF), while text objects (TextAB, TextBC, TextAC, etc.) display these lengths on the figure. Suitable for middle and high school geometry instruction, interactive classroom demonstrations, and pre-proof exploration of congruence criteria.