A rigid transformation, also known as an isometry, involves transformations that preserve the shape and size of a geometric figure. The properties that remain unchanged during a rigid transformation include:
- Distance: The distance between any two points remains the same.
- Angle: The angles between line segments remain unchanged.
- Size: The overall size of the shape does not change.
The types of rigid transformations include:
- Translation: Moving a shape from one location to another without changing its orientation.
- Rotation: Rotating a shape around a fixed point (the center of rotation) without changing its size or shape.
- Reflection: Flipping a shape over a line (the line of reflection) to create a mirror image without changing the size or shape.
While the orientation (the direction in which a shape faces) can change during a rigid transformation (specifically through rotation and reflection), the overall size and shape of the figure remain unchanged. Hence, a rigid transformation does not change the size or shape; it can change the position and orientation of the figure in a plane or space.
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