Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human’s intuitive reasoning about Euclidean geometry is not well
understood. The present study explores the cognitive processes and representations that support the
development of humans’ intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to
12-year-old children and 30 adults completed a localization task in which they visually extrapolated
missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even
young children’s visual extrapolations, only older children and adults reasoned about triangles in ways
that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and
reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry
may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to
reason using mental simulations of visual extrapolations.