Line symmetry, or just symmetry,
occurs when two halves of a figure mirror each other across a line.
The line of symmetry is the line
that divides the figure into two mirror images. A simple test to
determine if a figure has line symmetry is to fold the figure along the
supposed line of symmetry and see if the two halves of the figure
coincide.
Another name for the concept of line symmetry is reflection.
See An Intuitive Notion of Line
Reflections for further information on reflections.
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Nature displays line symmetry
in
some of its most beautiful work. The balanced
arrangement of symmetry creates pleasing and attractive
forms.
The white line is the line of
symmetry. |
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Many flowers possess
line symmetry. The
biologist's term for line symmetry is "bilateral
symmetry."
The white line is the line of
symmetry. |
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Mosaics and art work often demonstrate
the concept of reflections and line symmetry. This
drawing has two lines of
symmetry, as shown by the white lines. |
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This butterfly caterpillar displays
line symmetry.
The pink line is the line of symmetry. |
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Certain letters of the alphabet and
words possess line symmetry (such as the samples in the
photo).
Notice that some possess vertical line
symmetry, some possess horizontal line symmetry, and
some possess BOTH vertical and horizontal line symmetry. |
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Certain geometric figures possess line
symmetry. The figures in the photo are only a
sampling of the geometric figures which possess
symmetry.
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Are
people
symmetric?
Check
to see if
you are symmetric. Find a photograph of yourself
where you are looking straight ahead. Hold a
mirror perpendicular to the photo at the line of
symmetry for your face. How do you look? |
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Cutting the photo above on the line of
symmetry, and duplicating each side of the face,
produced the pictures you see here. The
tilt of the head accentuated these images. |
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In mathematics, we often
describe a concept like line symmetry with a formal definition.
It
may read something like the following:
Definition: A set of points has line
symmetry if and only if there is a line, l,
such that the reflection through l of
each point of the set is also a point of the set.
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Don't Panic!! |
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You do not have to memorize the definition above to
understand line symmetry. Just remember:
A figure has line
symmetry if there is a line on which the figure may be folded so that the
two parts of the figure will coincide.
