Given a geometric graph G = (V,E), where V is the set of vertices and E is the set of edges and a source-target pair {s,t} is a subset of V, a local geometric routing algorithm seeks a route from s to t using only local neighborhood relationships. This thesis proposes a local geometric routing algorithm that uses only a single state bit as message overhead and guarantees delivery of messages in three different classes of edge-augmented planar graphs: convex subdivisions, quasi planar convex subdivisions (allow some augmented edges on a spanning convex subdivision) and 2-augmented triangulations (allow some augmented edges on a spanning triangulation). The proposed algorithm is origin oblivious (does not require the knowledge of the origin vertex s) and predecessor oblivious (does not require the knowledge of the predecessor vertex).