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I think "isometries" and "rigid transformation" are two different names for the same thing. Look for "isometry" on wikipedia.

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I think "isometries" and "rigid transformation" are two different names for the same thing. Look for "isometry" on wikipedia.

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Preservation of Length

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Yes, that is correct.

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Because the glide reflection is a combination of two isometries, it is also an isometry.

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Rotations, reflections, and translations are all isometries while a dilation isn't because it doesn't preserve distance

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