Symmetry can greatly reduce the computational complexity and memory requirements of vast variety of geometric tasks. In this paper we propose a sweep-based algorithm to identify polylines satisfying local reflection symmetry to find skeletons of polygonal shapes. We describe the benefits and use cases of such polylines in shape segmentation, characterization, reconstruction, and generalized reflection symmetry computation. Finally, we demonstrate the robustness to noise and compare the results with other methods of skeleton computation.