Symmetry

A figure has symmetry if an isometry maps the figure onto itself.  A figure has line symmetry or reflectional symmetry if the isometry is a reflection.  The dashed lines in the figures below represent if and how many lines of reflectional symmetry the figure has.  Figure 4 is the only figure without reflectional symmetry.

ReflSymm

There is another type of symmetry a figure can posess.  Rotational symmetry maps a figure onto itself with a rotation of 180o or less.  If the figure has 180o rotational symmetry only, then it has point symmetry.  Figure 1 has 120o rotational symmetry.  Figure 2 has 90o rotational symmetry.  Figure 3 does not have rotational symmetry.  Figure 4 has 60o rotational symmetry.

RotationSymm 

Some figures will have both reflection and rotation symmetry, as does the square in both sets of figures.

 

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