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Here is a segment :
If we translate the segment up 5 units then down 5 units, it looks the same as it did originally.
A shape has symmetry if there is a rigid transformation which creates an image that fits exactly over the original shape. A shape has reflection symmetry if there is a reflection that takes the shape to itself, and the line of reflection in this case is called a line of symmetry. A regular hexagon has many lines of symmetry. Here are 2 of them. What other lines create a reflection where the image is the same as the original figure?
A line of symmetry is a line that divides a figure into two parts that are mirror images of each other. When a figure is reflected across one of its lines of symmetry, it takes the figure onto itself.
These dashed lines show two lines of symmetry for a regular hexagon, and two lines of symmetry for the capital letter I.
A figure has reflection symmetry if there is a reflection that takes the figure onto itself.
In this diagram, the letter X has reflection symmetry over each of the dashed lines.
A figure has symmetry if there is a rigid transformation that takes it onto itself. (This does not include transformations that take every point back to its original position.)