Isometry in geometry refers to transformations that maintain the original size and shape of figures, resulting in congruent shapes. These include translations, reflections, and rotations, which are classified as either orientation-preserving or orientation-reversing. Understanding these concepts is crucial for studying geometric congruence and symmetry.
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Isometry involves transformations that preserve distances between points, maintaining the original shape and size of geometric figures
Operations included in isometries
Isometries include translations, reflections, and rotations, but not dilations
Isometries result in two congruent figures, meaning they have the same size and shape
Translations move a figure without rotating or reflecting it, effectively sliding it to a new position while maintaining its orientation and size
Reflections create a mirror image of a figure across a line, preserving its size and shape
Rotations turn a figure around a fixed point by a certain angle without changing its size
These isometries maintain the cyclic order of a figure's vertices
These isometries flip the order of a figure's vertices, resulting in a mirror image
Isometries are crucial in comprehending how figures can be altered while preserving their fundamental characteristics
The three principal types of isometries are essential in maintaining the congruence of shapes
Mastery of isometries is vital in the study of geometry and topology, and is foundational for understanding congruence, symmetry, and shape properties
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Isometry Impact on Shape and Size
Preserves original shape and size; results in congruent figures.
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Types of Isometric Transformations
Includes translations, reflections, rotations; excludes dilations.
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Congruence in Isometries
Isometric figures are congruent; identical in size and shape.
