SSA Exploration – When Does the 'SSA Theorem' Hold?

①This interactive GeoGebra example dynamically demonstrates the non-uniqueness of triangles given two sides and a non-included angle (SSA), and explores under what conditions the SSA configuration uniquely determines a triangle. ②Core mathematical concepts include the SSA ambiguity in triangle congruence, the sine rule, triangle existence conditions, multiple solutions, and similarity transformations. ③Construction highlights: using GeoGebra commands such as Point, Segment, Rotate, Angle, Ray, Circle, and Intersect, the applet builds segments a and b, angles α and β, points A, B, C, D, E, circles c and d, rays f and g, and text objects text1, text2, text3, with rotation and circle intersections revealing different possible triangles. ④Suitable for high school geometry or introductory college geometry, this exploration helps students understand the sufficiency of congruence criteria and fosters critical thinking through dynamic investigation.