If you have no teeth you are edentulous. Example: "The edentulous dog at the Ford household posed no threat to the postman."
The word may not have much bite, but it has been in our vocabulary since the late 1700s. It comes from the Latin edentulus. It uses the prefix e- or ex- which meant missing or absent and the Latin dent- (tooth).
Other words using the dent- root include:
* dentist: the person who offers plastic toys for good brushing habits
* dentures: an artificial set of teeth
* dentifrice: a powder or paste for cleaning teeth
* denturist: someone who fits and repairs dentures