In addition to its uses as an experimental tool and a medium in which to model mathematical phenomena, dynamic geometry environments can help students develop mathematical ways of thinking, especially the habits that underlie analysis—reasoning by continuity and seeking invariants, for example. This talk will look at several classical geometric tasks, taken from a new high school program developed at EDC and from the recent translation into English of Hadamard's “Lessons in Geometry,” that lend themselves to this kind of analytic thinking when carried out in a dynamic envorinment.