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Here is a video explaining rigid motions and isometries

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Transformations and Isometries - Concept - Geometry Video by Brightstorm

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Time-saving video that describes all the different types of transformations in Geometry: dilations, rotations, translations, and reflections. Isometry is also described. Concept explanation.

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Some example images of rigid motions

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Difference Between Rigid Motions and Isometries

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Difference Between Rigid Motions and Isometries

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How to recognize the difference

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Can those two terms be used interchangeably?

asked Jul 23 '15 at 15:45

They are not the same thing, despite the confusion made by some textbooks (especially geometry textbooks for middle schools, for instance). Your right hand is isometric to your left hand, since there is a transformation preserving distances (the term isometry comes from Greek, the prefix iso stands for analogous and the suffix stands for distance) that brings your right hand into your left hand. However, there is no way to exactly overlap them, since they have different orientations (from which the right hand rule for computing $\omega\wedge r$, for instance). Less informally, a transformation of $\mathbb{R}^n$ is an isometry if the associated matrix is orthogonal (we can easily check that this is equivalent to preserving distances) and a rigid motion if, additionally, the determinant is $+1$.

answered Jul 23 '15 at 16:41

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What is the difference between a rigid motion and an isometry?

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Here is a website explaining isometries

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If a plane isometry has more than one fixed point, it must be either the identity transformation or a reflection. Every isometry of period two (two applications of the transformation preserving lengths in the original configuration) is either a reflection or a half-turn rotation.

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Here is a website telling you everything you need to know about rigid motions

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Any way of moving all the points in the plane such that a) the relative distance between points stays the same and b) the relative position of the points stays the same. There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.