Movements

A movement (isometry) of the plane is a transformation that preserves distances between all points. That is, for any two points $A$ and $B$, the distance between their images $A'$ and $B'$ after the movement is the same as the distance between $A$ and $B$.

Important properties

• Movements preserve lengths of segments and measures of angles.

• Movements map lines to lines and circles to circles.

• There are four main types: translations, rotations, reflections, and glide reflections.

• Movements are reversible: every movement has an inverse that is also a movement.