Reflection symmetry
symmetry with respect to a plane, when the shape does not change by reflecting all of its part from a mirror plane
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In two-dimensional space, there is a line/axis of symmetry, in three-dimensional space, there is a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric.
Symmetric function
In formal terms, a mathematical object is symmetric with respect to a given operation such as reflection, rotation, or translation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa).
The symmetric function of a two-dimensional figure is a line such that, for each perpendicular constructed, if the perpendicular intersects the figure at a distance 'd' from the axis along the perpendicular, then there exists another intersection of the shape and the perpendicular at the same distance 'd' from the axis, in the opposite direction along the perpendicular.
Another way to think about the symmetric function is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's mirror images. Thus, a square has four axes of symmetry because there are four different ways to fold it and have the edges all match.
The public source identifies “Reflection symmetry” as symmetry with respect to a plane, when the shape does not change by reflecting all of its part from a mirror plane. This brief keeps that definition visible, then builds a research path around Reflection, symmetry and respect.
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Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Jan 20, 2026. The linked authority identifier is Q15955882. None of the 0 selected statements returned an explicit reference.
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This entry incorporates text from “Reflection symmetry” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.