Reflections and Reflective Symmetry
The most familiar type of symmetry is reflective symmetry (also known as bilateral symmetry) which results from the transformation
called reflection.
Reflections occur across a line called the axis. To reflect a shape across an axis is to plot a special corresponding
point for every point in the original shape. Specifically, the
corresponding point is the point that is the same distance from
the axis as is the original point. You determine the distance
from a point to a line by drawing a line perpendicular to the
original line and that passes through the point.
A simple reflection of a point (red) across an axis to form another
point (blue). The dotted line is the perpendicular line used to
find distances. Notice that the distance from the red point to
the axis is the same as the distance from the blue point to the
axis.
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Here are several examples of reflections applied to entire shapes,
not just a single point. The original shape together with its
reflection is said to have reflective symmetry.
Examples of reflections and reflective symmetry
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A intuitive way to think about reflective symmetry is to imagine
the turning of the pages of a book. Suppose you could see through
the pages of a book. Then, when you turn a page, the part that
would show through would be the reflection of the original part.
How to visualize reflective symmetry
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What does it mean for a tessellation to have reflective symmetry?
If we can perform a reflection to a tessellation that such that
the result is the same as the original tessellation, then the
tessellation has reflectional symmetry. An example is as follows:
A tessellation that has reflective symmetry; the red dotted line
indicates one of the possible axes of reflection, and the gray
lines are the reflections of the black lines.
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 After trying the hands-on activity, use the templates on the templates
page to see why every regular, semiregular, and demiregular tessellations
has reflective symmetry. Use the technique that was explained in the hands-on
activity.
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