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- Recall from Postulates 4.1–4.3 and Theorem 4.1 that translations, refl ections, rotations, and compositions of these transformations are rigid motions.
static.bigideasmath.com/protected/content/ipe/aga22/aga22_geometry_ipe_04_04.pdf
May 4, 2022 · An identity motion is a rigid motion that moves an object from its starting location to exactly the same location. It is as if the object has not moved at all. There are four kinds of rigid motions: translations, rotations, reflections, and glide-reflections.
Transformations in geometry involve changing the position, size, or orientation of shapes. Rigid motions, a subset of transformations, only change the position and orientation without altering the size or shape. Examples of rigid motions include translations, rotations, and reflections.
Another name for a rigid motion or a combination of rigid motions is a congruence transformation because the preimage and image are congruent. The terms rigid motion and congruence transformation are interchangeable.
It turns out that all rigid transformations are in fact affine, but we shall not worry about that here. The matrix A is called the linear component, v the translation component of the transformation. A rigid transformation preserves angles as well as distances.
(1) Rigid Motions of the plane are transformations of the plane. This implies that a rigid motion T is has an inverse T-1, with T T-1= T-1T= I, the identity map. Note: Transformations have been key parts of geometry since the 19th century.
rigid motion transformations (translations, reflections, and rotations), and describe how a single rigid motion maps between congruent figures. They also learn that rigid motions preserve the size and shape of a figure, but that reflections change the orientation of the vertices of a figure. The next three lessons involve
RIGID MOTIONS: TRANSFORMATIONS THAT PRESERVE DISTANCE AND ANGLE MEASURE •If T is a rigid motion, always |T(A)T(B)| = |AB|. •If T is a rigid motion, always ∡T(A)T(B)T(C) = ∡ABC. •Rigid motions map lines to lines, since distinct points A, B, C are collinear if and only if ∡ABC = 0 or 180.
