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How do children’s developing intuitions about abstract figures on the Euclidean plane relate to geometries used for everyday navigation and object recognition? In a preregistered experiment, 300 4- to 9-year-old children watched dynamic videos of angles being drawn on an otherwise blank screen and were asked to indicate what happened next. Sparse and minimally different language framed these videos in different spatial contexts. Older children formed open shapes in the context of navigation but closed shapes in the context of object recognition. Visuals described using abstract language, moreover, elicited responses that resembled a combination of the navigation and object contexts. Geometry pedagogy may thus benefit from linking abstract concepts to children’s natural geometric intuitions used for navigation and object recognition.