<p>Non-degenerate conditions (NDGs) are essential prerequisites that ensure the validity of geometric theorems. While algebraic methods such as Wu’s method generate NDGs in polynomial form and provide geometric interpretations, these interpretations are often not expressed in terms of intuitive geometric quantities, such as lengths, angles, and areas, and instead remain peripheral annotations. Consequently, such NDGs are rarely integrated into the core geometric reasoning process. This paper proposes a methodology based on complex number identities to provide a unifying viewpoint for interpreting NDGs in the following settings. First, we systematically transform algebraic NDGs into expressions involving explicit geometric quantities, thereby incorporating them more directly into the reasoning chain. Second, by leveraging these geometric-quantity-based NDGs, we progressively connect the given conditions to the conclusion, ultimately deriving complex number identities that unify the original theorem, its converse, and quantitative extensions. Experimental evaluation on over 100 geometric problems, including classical theorems and Olympiad-level challenges, indicates that more than 90% of the cases tested within our candidate library admit meaningful geometric interpretations and enable proposition reconstruction. Notably, more than ten of the derived extended results have been accepted as problem proposals in international mathematical journals such as Crux Mathematicorum, providing additional evidence of their mathematical interest. This work enhances the interpretability and educational value of machine-generated proofs and suggests a possible direction for intelligent problem generation and automated geometric reasoning.</p>