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Greedy geographic routing is an attractive localized routing scheme for wireless sensor networks due to its efficiency and scalability. However, greedy geographic routing may fail due to routing voids on random network topologies. We study greedy geographic routing in an important class of wireless sensor networks (e.g., surveillance or object tracking systems) that provide sensing coverage over a geographic area. Our analysis and simulation results demonstrate that an existing geographic routing algorithm, greedy forwarding (GF), can successfully find short routing paths based on local states in sensing-covered networks. In particular, we derive theoretical upper bounds on the network dilation of sensing-covered networks under GF. We also propose a new greedy geographic routing algorithm called Bounded Voronoi Greedy Forwarding (BVGF) that achieves path dilation lower than 4.62 in sensing-covered networks as long as the communication range is at least twice the sensing range. Furthermore, we extend GF and BVGF to achieve provable performance bounds in terms of total number of transmissions and reliability in lossy networks.