Let $m$ be an isometry in euclidean plane that changes orientation. Prove that $m \circ m$ is a translation.I do not have an idea how to start the proof of this exercise.
2026-03-26 14:43:14.1774536194
are isometries on euclidean plane translations
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The orientation-reversing isometries of the Euclidean plane are the reflections and glide reflections. If you apply a reflection twice, you get back the original shape so the translation is trivial. Now, what happens in the other case?