Although Wu’s method has achieved remarkable success in automated geometric theorem proving, its proving process relies heavily on complex algebraic elimination operations, making it difficult to directly reveal the reasoning relationships between hypotheses and conclusions, thereby reducing the interpretability and readability of the resulting proofs. To address this issue, this paper presents a theoretical reconstruction of the proving mechanism of Wu’s method from the perspective of identity proofs. By establishing an identity representation between the conclusion polynomial and the hypothesis polynomials, the algebraic elimination process of Wu’s method is transformed into a structured proof representation with explicit logical semantics. To this end, a Remainder Tracking Matrix (RTM) is introduced, and a systematic method is designed for the joint construction of the characteristic sequence and its RTM during the ascending process, thereby providing a structured and traceable algebraic representation for the elimination procedure of Wu’s method. Furthermore, we realize a mechanized construction of identity proofs within Wu’s method, demonstrating its capability in constructing readable proofs. Additionally, we demonstrate the effectiveness and feasibility of the proposed approach via machine-assisted verification of several representative geometric theorems. This study offers a new pathway toward the structured representation of geometric proofs in Wu’s method and lays a theoretical foundation for the algebraic characterization of geometric invariants as well as for enhancing the explainability of automated geometric theorem proving.