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{"embedding_dim": 1024, "data": [{"__id__": "rel-bcfe4067a78db61c5e344a3c6067e9c1", "__created_at__": 1752211508, "src_id": "Point D", "tgt_id": "Triangle ABC", "content": "Point D\tTriangle ABC\ngeometric construction,triangle extension\nPoint D is constructed from triangle ABC by extending AB and adding segment BD equal to BC.", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-34f26cf67f89c41e368f995769f3bee1", "__created_at__": 1752211508, "src_id": "Euclid's Fifth Postulate", "tgt_id": "Point D", "content": "Euclid's Fifth Postulate\tPoint D\nangle comparison,geometric proof\nEuclid's Fifth Postulate is used to compare angles in triangle ACD, which includes point D.", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-469520e112344d64d841d843cec91e06", "__created_at__": 1752211508, "src_id": "Proposition 19 of the Elements", "tgt_id": "Triangle ABC", "content": "Proposition 19 of the Elements\tTriangle ABC\nangle-side relationship,geometric theorem\nProposition 19 is applied to triangle ABC to justify the relationship between angles and sides.", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-5b3cdf18806473ee2a2fc55a7b0fd944", "__created_at__": 1752211508, "src_id": "Point P", "tgt_id": "Triangle ABC", "content": "Point P\tTriangle ABC\nangle proof,interior point\nPoint P is an interior point of triangle ABC, used to demonstrate angle relationships within the triangle.", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-e3c9f606eb2d48c5e37f2c2d8bff69ed", "__created_at__": 1752211508, "src_id": "三角不等式", "tgt_id": "三角形ABC", "content": "三角不等式\t三角形ABC\n几何定理,边角关系\n三角不等式直接应用于三角形ABC的三边关系证明。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-f7bcf1a714c6122abc696165fc098924", "__created_at__": 1752211508, "src_id": "三角形ABC", "tgt_id": "欧几里得第五公理", "content": "三角形ABC\t欧几里得第五公理\n公理应用,角度推导\n第五公理用于比较三角形ACD中的角度与三角形ABC的构造相关。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-6e53094235679e936c94ad45593f0f62", "__created_at__": 1752211508, "src_id": "几何原本", "tgt_id": "命题19", "content": "几何原本\t命题19\n定理引用,数学经典\n命题19源自《几何原本》是证明边角关系的理论来源。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-37c38a5bb6bf0a593501536eddae56c6", "__created_at__": 1752211508, "src_id": "三角形ABC", "tgt_id": "命题19", "content": "三角形ABC\t命题19\n几何推理,边角逻辑\n命题19被用于证明三角形ABC中边AD与边AC的关系。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-37e6f8ce2b52adfdbedbf5458829145f", "__created_at__": 1752211508, "src_id": "三角形ABC", "tgt_id": "点D", "content": "三角形ABC\t点D\n几何扩展,辅助构造\n点D是三角形ABC的延伸构造用于辅助证明边角不等式。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-6144c8f85132b7365b9799eef55d09c1", "__created_at__": 1752211508, "src_id": "三角形ABC", "tgt_id": "点P", "content": "三角形ABC\t点P\n内部角度,几何性质\n点P的存在证明了三角形内部点的角与顶角的关系。", "source_id": "chunk-75b23a7e22383153b011bd3d121184f0", "file_path": "unknown_source"}, {"__id__": "rel-c1933338c2519d138024b54332ba34fa", "__created_at__": 1752211508, "src_id": "AC", "tgt_id": "BP", "content": "AC\tBP\ngeometric construction,intersection\nBP intersects AC at point D, forming geometric relationships.", "source_id": "chunk-e2c7bd24a26246e194d4d56ab2ed22f1", "file_path"