The study aimed to examine cognitive behaviors and the corresponding brain areas via functional magnetic resonance imaging (fMRI) while people categorize geometrical figures. The results showed categorization tasks, positive/negative examples, and typicality interactively influenced reaction times. It indicates that the effects of one variable were not constant across different variables. For instance, the reaction times (RTs) in the typical examples were not quicker, in all conditions, than that in the atypical examples. It may be the results of filtering out the accuracy below 98%. However, the corresponding brain areas were only found for the categorization tasks. Both “Triangles” and “Quadrangles” categorization tasks deactivated the posterior cingulated cortex and there were significantly overlapped areas in BA31. “Quadrangles” categorization task additionally deactivated superior temporal lobes (BA41) and premotor areas (BA6) but “Triangles” did not. The results suggested the retrieval of geometrical concepts and the comparison to the stimuli examples would be associated with the posterior cingulated cortex, which may be independent from the processing of stimuli examples.