English:
A given translation ${\displaystyle {\mathit {T}}}$  may be decomposed into two reflections with parallel axis:  two lines here named  Δ ₁  and  Δ ₂ .  If one of the reflections  ${\displaystyle {\mathit {R}}_{\,1}}$  or  ${\displaystyle {\mathit {R}}_{\,2}}$  is given, the axis of which is perpendicular to the direction of ${\displaystyle {\mathit {T}},}$  the other reflection is unique which fulfills the equality:  ${\displaystyle {\mathit {R}}_{\,2}~\circ ~{\mathit {R}}_{\,1}~=~{\mathit {T.}}}$  There is a unique translation ${\displaystyle {\mathit {S}}}$  that transforms Δ ₁  into  Δ ₂ ,  then   ${\displaystyle {\mathit {S}}^{\,2}~=~{\mathit {T}},}$   ${\displaystyle \mathrm {and\quad } {\mathit {S}}^{\,-\,2}~=~{\mathit {T}}^{\,-\,1}~=~{\mathit {R}}_{\,1}~\circ ~{\mathit {R}}_{\,2}.}$ The trapezoid ABCD  is part of the tiling of the top of the drawing, where the triangular elements are green and yellow. Across the line Δ ₁,  the tiling and ABCD  are transformed by the reflection ${\displaystyle {\mathit {R}}_{\,1},}$  the trapezoid ABCD  becomes  A ₁ B ₁ C ₁ D ₁ ,  and the elements of the tiling become blue and gray as in this image or this other one. The image of ABCD  through the translation ${\displaystyle {\mathit {T}}}$  is the trapezoid  A ₂ B ₂ C ₂ D ₂ ,  that is filled by three elements of the first tiling, one green triangle and two yellow.