This paper proposes a conceptual framework to classify ontological beliefs on elementary geometry. As a first application, this framework is used to interpret nine interviews taken from secondary school teachers. The interpretation leads to the following results: (a) the ontological beliefs vary in a broad range, denying the assumption that a similar education provokes analogue opinions; and (b) ontological beliefs have a remarkable influence on the standards of proofs and on the epistemological status of theorems, and also on the role of drawing, constructions and their descriptions, media, and model building processes.
