My teacher say that they are the same thing because the transformation that they both preserve distance and measurement of angels but just the isometry have opposite isometry and direct isometry, where the opposite isometry doesn't preserve the oreientation. So are they still the same?
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$\begingroup$To echo the comments, first, it does indeed depend on the local definitions. What your teacher meant by "rigid motion" is probably an orientation-preserving isometry.
For a mundane example: if you have a pair of gloves, there is an isometry which transforms the left-hand glove into the right-hand one (think of mirror image), but there is no such "rigid motion" (as anyone knows who ever tried to put a glove on the wrong hand).
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