Topology control is to determine the transmission power of each node so as to maintain network connectivity and consume the minimum transmission power. Cooperative Communication (CC) is a new technology that allows multiple nodes to simultaneously transmit the same data. It can save transmission power and extend transmission coverage. However, prior research work on topology control considers CC only in the aspect of energy saving, not that of coverage extension. We observe that CC can bridge (link) disconnected networks and therefore identify the challenges in the development of a centralized topology control scheme, named shape Cooperative Bridges, which reduces transmission power of nodes as well as increases network connectivity. We propose three algorithms that select energy efficient neighbor nodes, which assist a source node to communicate with a destination node: an optimal method and two greedy heuristics. In addition, we consider a distributed version of the proposed topology control scheme. Our findings are substantiated by an extensive simulation study, through which we show that the shape Cooperative Bridges scheme substantially increases the connectivity with tolerable increase of transmission power compared to other existing topology control schemes, which means that it outperforms in terms of a connectivity-to-power ratio.