Side-Side-Angle (SSA) Triangle Ambiguity and Cosine Theorem Dynamic Demo

This GeoGebra example dynamically illustrates the ambiguity of triangle construction under the Side-Side-Angle (SSA) condition, where two sides and a non-included angle are given. It demonstrates how the same SSA data can yield zero, one, or two possible triangles, and connects this to the cosine theorem for solving triangles. Core mathematical concepts include triangle congruence criteria, the SSA ambiguous case, the law of cosines, and the incircle of a triangle. The construction uses Point commands to create points A, B, C, D, E, F, Segment commands for lines f, g, h, i, j, k, and Angle commands to label angles α, β, γ, δ, ε, ζ. By dragging points, users can explore how changing the given side lengths or the included angle affects the number of valid triangles)Skip, and observe the incircle and arithmetic mean relationships. This resource is ideal for high school geometry, math competitions, or introductory college geometry courses, helping students grasp why SSA is not a valid congruence theorem and how the cosine theorem resolves triangle ambiguity.