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Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognise, because one half is the reflection of the other half.
Here my dog "Flame" has her face made perfectly symmetrical with a bit of photo magic.
The white line down the center is the Line of Symmetry
The reflection in this lake also has symmetry, but in this case:
The Line of Symmetry (also called the Mirror Line) does not have to be up-down or left-right, it can be in any direction. But there are four common directions, and they are named for the line they make on the standard XY graph.
See these examples (the artwork was made using Symmetry Artist) :