Will my rescued dogs eat my cat?

I rescued a basset/beagle and a wire haired terrier. I’ve had them for more than 2 years. They have been separated from my cat. (The cat lives upstairs and the dogs downstairs). Besides feeding them close together, what else should I be doing so the entire family can be in the room together? I have taken the dogs upstairs on leashes, but they become very aggressive while searching out the cat. Needless to say, the cat has hidden and is now traumatized. (He hides under the blankets as if no one can see or smell the huge lump!) Help!!!