Constructing online vectorized High-Definition (HD) maps is critical for downstream prediction and planning. Recent efforts have built strong baselines for this task, however, geometric shapes and relations of instances in road systems are still under-explored, such as parallelism, perpendicular, rectangle-shape, etc. In our work, we propose GeMap (Geometry Map), which end-to-end learns Euclidean shapes and relations of map instances beyond fundamental perception. Specifically, we design a geometric loss based on angle and magnitude clues, robust to rigid transformations of driving scenarios. To address the limitations of the vanilla attention mechanism in learning geometry, we propose to decouple self-attention to handle Euclidean shapes and relations independently. Our method achieves new state-of-the-art performance on the nuScenes and Argoverse 2 datasets. Remarkably, it reaches a 71.8% mAP on the large-scale Argoverse 2 dataset, outperforming MapTRv2 by +4.4% and surpassing the 70% mAP threshold for the first time. The code will be available.