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Summary
DescriptionAcadem Reflections with parallel axis on wallpaper.svg
English: A given translation may be decomposed into two reflections with parallel axis: two lines here named Δ 1 and Δ 2 . If one of the reflections or is given, the axis of which is perpendicular to the direction of the other reflection is unique which fulfills the equality: There is a unique translation that transforms Δ 1 into Δ 2 , then
The trapezoidABCD 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 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 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.
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A wallpaper covers a half‑plane of edge Δ1. Its reflection under R1 with respect to Δ1 has other colors. Reflection R1 transforms trapezium ABCD into A1B1C1D1, itself reflection of A2B2C2D2 with respect to Δ2. Δ2 ∕∕ Δ1. U transforms Δ1 into Δ2.
Un papier peint recouvre un demi‑plan de bord Δ1. Son symétrique par rapport à Δ1 a d’autres couleurs. La symétrie R1 d’axe Δ1 transforme le trapèze ABCD en A1B1C1D1, image de A2B2C2D2 par la symétrie R2 d’axe Δ2. Δ2 ∕∕ Δ1. U transforme Δ1 en Δ2.