Exploring the SSA Ambiguous Case of Triangle Congruence

This example demonstrates constructing triangles given two sides and a non-included angle (SSA) and illustrates the ambiguous case where zero, one, or two possible solutions may exist. Core mathematical concepts include the limitation of triangle congruence criteria, the Law of Sines, the relationship between angles and sides, and existence analysis in geometry. The construction uses GeoGebra commands such as Point, Rotate, Angle, Intersect, Polygon, Segment, Ray, and If. Sliders control sides a, b, and angle α, drawing rays and arcs, finding intersections to obtain possible vertices C, and dynamically displaying the results. Suitable for high school geometry teaching, mathematical modeling courses, or elementary triangle construction seminars, it can be used for teacher demonstrations, classroom exploration, or student independent inquiry.