In this paper, a novel design of planar dual-band multi-way lossless power dividers (PDs), namely Bagley Polygon PDs, is presented. The proposed PDs use Π-type dual-band transformers as basic elements, whose design formulas are analyzed and simplified to a concise form. The equivalent circuit of the dual-band Bagley Polygon PD is established, based on which design equations are derived mathematically. After that, the design procedure is demonstrated, and special cases are discussed. To verify the validity of the proposed design, 3-way and 5-way examples are simulated and fabricated at two IMT-Advanced bands of 1.8 GHz and 3.5 GHz, then simulation and measurement results are provided. The presented PDs have good performances on the bandwidths and phase shifts. Furthermore, the planar configuration leads to convenient design procedure and easy fabrication.