While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances.This paper identifies the importance of being geometry-aware for semantic correspondence and reveals a limitation of the features of current foundation models under simple post-processing.We show that incorporating this information can markedly enhance semantic correspondence performance with simple but effective solutions in both zero-shot and supervised settings. We also construct a new challenging benchmark for semantic correspondence built from an existing animal pose estimation dataset, for both pre-training validating models. Our method achieves a PCK@0.10 score of 65.4 (zero-shot) and 85.6 (supervised) on the challenging SPair-71k dataset, outperforming the state of the art by 5.5p and 11.0p absolute gains, respectively.Our code and datasets are publicly available at: https://telling-left-from-right.github.io.