In traditional Euclidean geometry, space all equiangular polygons v an odd number of sides also equilateral?

It is easy to prove the all equiangular triangle are likewise equilateral using straightforward trogonometric rules.

You are watching: Equiangular polygon that is not equilateral

On the various other hand, the is basic to conceive of an equiangular quadrilateral the is no equilateral, i.e. A rectangle.

Extending this further, I can easily develop of an equiangular hexagon that is not equilateral, but I haven"t to be able come visualize one equiangular pentagon that is likewise equilateral:

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Is this true that all equiangular polygons with an odd number of sides also equilateral? If so, is over there a straightforward method to prove it? If not, is over there a counterexample, one equiangular polygon with an odd number of sides that is no equilateral?


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asked january 1 "12 at 23:41
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Peter OlsonPeter Olson
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No they"re not. Simply take your continuous pentagon, and pull that is base down while maintaining the angles. It will get much shorter as its surrounding edges acquire longer.


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answered jan 1 "12 at 23:47
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TonyKTonyK
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No. If you take your continual pentagon, because that example, you can slide one of the sides away from the facility without changing its direction, and also extend its two neighbor sides appropriately. This provides the chosen side shorter, two various other sides longer, but leaves the angle intact.


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answered jan 1 "12 in ~ 23:48
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hmakholm left end Monicahmakholm left over Monica
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