In this report we explore the connection between the local form and transitions of the symmetry set, on the one hand, and those of the medial axes and shocks, on the other. In particular, we determine a local description of the medial axes and shocks as subsets of the symmetry set in 2D. The 3D case is treated in a sequel [Giblin:Kimia;lems171;1998]. In addition, we derive the complete transitions of the medial axes and the shock set in a one-parameter family of deformations in 2D. These transitions are crucial for robust recognition in vision where shapes undergo arbitrary deformations both as continuous changes and as abrupt transitions due to changes in the viewing geometry and object deformations. We also relate the local form of boundaries as a function of the local form of axes and thus derive intrinsic reconstruction formulas for the boundaries from skeletal representations. We illustrate formal derivations with numerical simulations and discuss their significance for object recognition.