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Description: At the scale in which we live, space is continuous. Nevertheless, our perception and cognition parse the world into categories, whether physical, like scene or object, or abstract, like infinitesimal point or 7. The present study focuses on 2 categories of special angles in planar geometry, parallels and perpendiculars, and we evaluate how these categories might be reflected in adults’ basic angle discrimination. In the first experiment, participants were most precise when detecting 2 parallel or perpendicular lines among other pairs of lines at different relative orientations. Detection was also enhanced for 2 connected lines whose angle approached 90°, with precision peaking at 90°. These patterns emerged despite large variations in the scales and orientations of the angle exemplars. In the second experiment, the enhanced detection of perpendiculars persisted when stimuli were rotated in depth, indicating a capacity to discriminate shapes based on perpendicularity in 3 dimensions despite large variation in angles’ 2-dimensional projections. The results suggest that 2 categorical concepts which lie at the foundation of Euclidean geometry, parallelism and perpendicularity, are reflected in our discrimination of simple visual forms, and they pave the way for future studies exploring the developmental and evolutionary origins of these cognitive categories.