Recognition of geometrical patterns seems to be an important aspect of human intelligence. Geometric pattern recognition is used in many intelligence tests, including Dehaene’s odd-oneout test of Core Geometry (CG)) based on intuitive geometrical concepts (Dehaene et al., 2006). Earlier work has developed a symmetry-based cognitive model of Dehaene’s test and demonstrated performance comparable to that of humans. In this work, we further investigate the role of symmetry in geometrical intuition and build a cognitive model for the 2- Alternative Forced Choice (2-AFC) variation of the CG test (Marupudi & Varma 2021). In contrast to Dehaene’s test, 2- AFC leaves almost no space for cognitive models based on generalization over multiple examples. Our symmetry-based model achieves an accuracy comparable to the human average on the 2-AFC test and appears to capture an essential part of intuitive geometry.