Gordon, Cameron, 1945-2009-11-052017-05-112009-11-052017-05-112009-08http://hdl.handle.net/2152/6682textThis dissertation is an investigation into the classification of all hyperbolic manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3. The first example was given by Boyer and Zhang. They used the Whitehead link. Eudave-Muñoz and Wu gave an infinite family of such hyperbolic manifolds using tangle arguments. I show in this dissertation that these are the only hyperbolic manifolds admitting a reducible Dehn filling and a toroidal Dehn filling with distance 3. The main tool to prove this is to use the intersection graphs on surfaces introduced and developed by Gordon and Luecke.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Reducible Dehn fillingToroidal Dehn fillingDistance 3Whitehead linkHyperbolic manifoldsTangle arguments