This study explored whether people create Euclidean representations of 2-dimensional right triangles from touch and use them to make spatial inferences in accord with Euclidean distance axioms. Blindfolded participants who were instructed to form visual images of triangles felt the vertical and horizontal sides of right triangles, then estimated the lengths (but not the angles) of the 3 triangle sides. In these 3 experiments, length estimates conformed closely to the Euclidean metric when evaluated on application of the Pythagorean theorem. Participants who used a visual imaging strategy were accurate more often than those who used visual imagery less often. In Experiments 2 and 3, a hypotenuse inference was as accurate as a direct haptic judgment of the hypotenuse. These results demonstrated similar accuracy of the hypotenuse judgments when participants made verbal rather than haptic estimates. The findings indicate that participants can form Euclidean representations under certain conditions from felt 2-dimensional right triangles based on visual images.