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:


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?

asked january 1 "12 at 23:41

Peter OlsonPeter Olson
2,16511 yellow badge2020 silver badges3737 bronze title
include a comment |

2 answer 2

active earliest Votes
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.

answered jan 1 "12 at 23:47

57.8k44 gold badges7575 silver badges162162 bronze badges
include a comment |
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.

point out
answered jan 1 "12 in ~ 23:48

hmakholm left end Monicahmakholm left over Monica
273k2222 yellow badges391391 silver badges646646 bronze title
include a comment |

your Answer

Thanks for contributing solution to betterworld2016.orgematics Stack Exchange!

Please be sure to answer the question. Carry out details and share her research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; back them increase with references or personal experience.

Use betterworld2016.orgJax to format equations. betterworld2016.orgJax reference.

To discover more, check out our advice on writing great answers.

See more: Colors Of Stars Of Which Color Have The Highest Surface, General Astronomy/Temperature

Draft saved
Draft discarded

Sign increase or log in in

sign up using Google
sign up utilizing Facebook
authorize up using Email and Password

Post together a guest

email Required, but never shown

Post together a guest


Required, however never shown

short article Your prize Discard

By click “Post your Answer”, you agree to our regards to service, privacy policy and cookie plan

Not the prize you're spring for? Browse various other questions tagged geometry or ask your own question.

The Overflow Blog
Featured ~ above Meta
Is it possible for a form to have actually equal angles yet not same sides/ evil versa?
Action that the symmetry team on polygons
Equiangular polygon inscriptions in rectangle
Is an equilateral triangle the very same as an equiangular triangle, in any type of geometry?
meaning of rectangle
present that if a convex pentagon is equilateral, and also two of its nearby inner angles measure 108 degree, then the pentagon is equiangular.
all the 2-d polygon that have the right to be offered to kind 3-d polyhedrons
What is the maximum number of consecutive sides whose lengths you can select without uniquely determining the polygon?
hot Network questions an ext hot concerns

concern feed
subscribe to RSS
question feed To i ordered it to this RSS feed, copy and paste this URL right into your RSS reader.

ridge Exchange Network
site architecture / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.29.40598

betterworld2016.orgematics ridge Exchange works best with JavaScript allowed

your privacy

By click “Accept every cookies”, friend agree stack Exchange can store cookie on your an equipment and disclose details in accordance through our Cookie Policy.