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Lines of Symmetry

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

What are lines of symmetry?

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
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Associated Topics:
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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