← GeoProof

Drag triangle ABC, the two square handles that define the mirror line m, or the amber handle that sets the glide distance. The image A double-prime B double-prime C double-prime is the triangle reflected across m and then slid along it by a vector parallel to m. This is the fourth plane isometry: orientation is reversed and there is no fixed point. The midpoint of every point and its image lands exactly on the mirror line. Toggles show the reflection step, those midpoints, and the result of applying the glide reflection twice, which is a pure translation. An info button opens a drawer explaining the theorem.

glide reflection = reflect across m, then slide by v (∥ m)
Drag the triangle, the square mirror handles, or the amber handle to change the glide distance.