What is a rigid motion in geometry?

In geometry, a rigid motion is a transformation that preserves distances and angles. This means that when an object is subjected to a rigid motion, its size and shape do not change. Rigid motions include translations, rotations, and reflections.

Translations involve moving an object along a straight line without changing its orientation. Rotations involve turning an object around a fixed point by a certain angle. Reflections involve flipping an object across a line, known as the line of reflection.

Rigid motions are important in geometry because they allow us to describe how shapes can be transformed without altering their fundamental properties. They are often used to prove geometric theorems, solve geometric problems, and analyze geometric objects.

Rigid motions are also known as isometries because they preserve distances. Isometries play a crucial role in geometry and have applications in various fields, such as computer graphics, robotics, and physics.