Retrieval-Augmented Generation (RAG) mitigates hallucination in large language models (LLMs) by incorporating external knowledge during generation. However, the effectiveness of RAG depends not only on the design of the retriever and the capacity of the underlying model, but also on how retrieved evidence is structured and aligned with the query. Existing RAG approaches typically retrieve and concatenate unstructured text fragments as context, which often introduces redundant or weakly relevant information. This practice leads to excessive context accumulation, reduced semantic alignment, and fragmented reasoning chains, thereby degrading generation quality while increasing token consumption. To address these challenges, we propose Tri-RAG, a structured triplet-based retrieval framework that improves retrieval efficiency through reasoning-aligned context construction. Tri-RAG automatically transforms external knowledge from natural language into standardized structured triplets consisting of Condition, Proof, and Conclusion, explicitly capturing logical relations among knowledge fragments using lightweight prompt-based adaptation with frozen model parameters. Building on this representation, the triplet head Condition is treated as an explicit semantic anchor for retrieval and matching, enabling precise identification of query-relevant knowledge units without directly concatenating lengthy raw texts. As a result, Tri-RAG achieves a favorable balance between retrieval accuracy and context token efficiency. Experimental results across multiple benchmark datasets demonstrate that Tri-RAG significantly improves retrieval quality and reasoning efficiency, while producing more stable generation behavior and more efficient resource utilization in complex reasoning scenarios.