Triangle Congruence under SSA: Uniqueness vs Two Solutions

This example demonstrates how triangle congruence behaves when the given information follows the SSA condition (two sides and a non-included angle). It highlights the key phenomenon that SSA does not guarantee a unique triangle: depending on the side lengths and the angle, there may be no triangle, exactly one triangle, or two distinct triangles that satisfy the same measurements. The central math concepts are triangle congruence tests, the SSA (side–side–angle) ambiguity, and triangle existence/number of solutions driven by the given constraints. Construction-wise, the provided GeoGebra “construction summary” is empty, so the model should be built by creating the required geometric objects (segments for the two given sides, an angle ray for the given non-included angle), imposing constraints, and generating all valid configurations while visualizing how solution branches appear or disappear as parameters change. This is well-suited for middle/high school geometry lessons, dynamic-geometry demonstrations, and student investigations focused on understanding why SSA differs from ASA/AAS in uniqueness.