Today in class a student observed and asked the following:
While the diagonal of a rectangle is not a line of symmetry, it does cut the rectangle into two congruent parts. This is a noteworthy property. Is there a name for this kind of line segment (one that cuts a closed plane figure into two new congruent closed plane figures)?
This stumped me. It also brought to mind a more general question: Is there a name for a line segment that cuts a closed plane figure into two new closed plane figures with equal area?
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$\begingroup$A line that cuts a polygon into two congruent polygons does not necessarily correspond to a symmetry of the original polygon. Consider e.g.
A line that cuts a plane region into regions of equal area is sometimes called an area bisector of the region.
$\endgroup$ $\begingroup$A line of symmetry *including rotational symmitry as Doug M observes above ) always divides a figure into two symmitrical parts which will be called congruent figures in case the initial figure was a closed figure.
Is every line which divides thus a line of symmetry....i leave that question for now
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