Symmetry in traffic patterns is a fundamental aspect of intelligent transportation systems, aiming to precisely predict traffic flow in real time despite the complex interplay of spatial and temporal factors. This paper presents a novel method of traffic forecasting that incorporates parameters related to road symmetry into a Graph Convolution Network model. Our model is crafted to dynamically adjust to real-time changes in road conditions, including the presence of symmetric and asymmetric road layouts, which substantially influence traffic flow. We have developed a GCN model that not only accounts for standard traffic flow metrics but also integrates a matrix representing road symmetry. The model undergoes training and validation on the METR-LA dataset, showcasing a significant enhancement in prediction accuracy. In the comparative analysis of state-of-the-art methods, our model demonstrated a significant enhancement in performance, achieving 30.68% improvement in Mean Squared Error (MSE) and a 24.28% improvement in Mean Absolute Error (MAE) over the best-performing method. The implications of our research are profound for urban planners, traffic management systems, and navigation service providers, as it offers a more dependable tool for forecasting traffic conditions, aiding in road design, and refining route planning strategies based on the symmetry of road networks.