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### Lines of Symmetry

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Date: 03/17/97 at 20:19:46
Subject: Lines of Symmetry

What are lines of symmetry?
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```
Date: 03/18/97 at 14:00:18
From: Doctor Rob
Subject: Re: Lines of Symmetry

A line of symmetry is an imaginary line drawn through a plane figure
such that if the figure is flipped over using that line as an axis of
rotation, you get the same figure back again.

A simple example is an isosceles triangle. Suppose that you orient the
figure so that the odd side (length not equal to the other two, which
are equal to each other) is horizontal, and the opposite vertex is
above it. Then the line of symmetry is the altitude from that vertex
down to that odd side. It is not part of the original figure, which is
why I called it imaginary, but it is easy to construct. If you flip
the triangle over using this altitude as an axis of rotation, the
equal sides will be swapped, the equal base angles will be swapped,
the vertex angle will be left alone, and the base will be left in
place.  You will get an identical copy of the original figure.

Another, more complicated example is a square. There are four lines of
symmetry. Two are the diagonals of the square, and two are the
perpendicular bisectors of the sides. Can you see why? These lines
are not part of the original figure, but are constructed from it.

If you need more explanation, write again and we'll try harder.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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