Definition
Rigid transformation
A rigid transformation moves or flips a figure without changing any distance, angle measure, shape, or size.
What it means
Think of a shape cut from firm card. You may slide it, turn it around a point, or flip it over, but you may not stretch, squash, or resize it. Wherever the cutout ends up, all its side lengths and angles still match the starting shape. That kind of move is rigid.
Remember it
Move it like a cardboard cutout: slide, turn, or flip—never stretch.
Example
Start with a right triangle whose side lengths are 3, 4, and 5 units. Slide it 6 units right, turn it 90°, or reflect it across a line. Its three side lengths are still 3, 4, and 5, so every image is congruent to the original.
Watch for
A dilation with scale factor 2 is not rigid because every distance doubles. A dilation with scale factor 1 leaves all distances unchanged, so it is rigid but produces no change in size.
Common mix-up
Rigid does not mean the figure stays still. It may move, turn, or flip; rigid means its internal distances and angles do not change.
Exact meaning
A rigid transformation is a transformation that preserves the distance between every pair of points. It therefore preserves segment lengths and angle measures and maps a figure to a congruent image. Translations, rotations, reflections, and any sequence of them are rigid transformations.