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

It is basic to prove that all equiangular triangles are also equilateral using simple trogonometric rules.

You are watching: Equilateral polygon that is not equiangular

On the other hand, it is straightforward to conceive of an equiangular quadrilateral the is not equilateral, i.e. A rectangle.

Extending this further, I have the right to easily develop of one equiangular hexagon the is no equilateral, but I haven"t been able to visualize one equiangular pentagon that is additionally equilateral:

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

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asked january 1 "12 at 23:41

Peter OlsonPeter Olson
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No they"re not. Simply take your regular pentagon, and pull the base under while keeping the angles. It will certainly get much shorter as its nearby edges obtain longer.

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answered jan 1 "12 at 23:47

TonyKTonyK
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No. If you take it your regular pentagon, for example, you can slide among the sides away from the center without transforming its direction, and extend its two neighbor sides appropriately. This makes the liked side shorter, two other sides longer, however leaves the angles intact.

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answered jan 1 "12 at 23:48

hmakholm left end Monicahmakholm left over Monica
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