SSS Congruence: Constructing and Verifying Triangles with Three Equal Sides

This GeoGebra example demonstrates the SSS (Side-Side-Side) congruence criterion by constructing two triangles with corresponding sides equal and verifying that their angles match. The core mathematical concept is the triangle congruence theorem: if three sides of one triangle are equal to three sides of another, the triangles are congruent. The construction uses GeoGebra commands such as Point, Segment, Circle, Line, Intersect, Angle, and Distance. It starts by drawing triangle ABC with sides a, b, c, then creates circles with radii d, e, f (equal to the given side lengths) to locate the second triangle DEF via circle intersections. The angles α, β, γ and δ, ε, ζ are measured, along with distance AD, and text objects text1 and text2 display the congruence conclusion. This is ideal for middle school or high school geometry lessons to visually explore congruence criteria and geometric construction techniques.