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?


geometry
re-publishing
mention
monitor
asked january 1 "12 at 23:41
*

Peter OlsonPeter Olson
2,16511 gold badge2020 silver badges3838 bronze title
$endgroup$
2
include a comment |

2 answers 2


energetic earliest Votes
9
$egingroup$
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.


re-publishing
cite
monitor
answered jan 1 "12 at 23:47
*

TonyKTonyK
57.9k44 yellow badges7575 silver- badges162162 bronze title
$endgroup$
2
include a comment |
1
$egingroup$
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.


re-superstructure
point out
monitor
answered jan 1 "12 at 23:48
*

hmakholm left end Monicahmakholm left over Monica
274k2222 gold badges392392 silver- badges646646 bronze title
$endgroup$
include a comment |

her Answer


Thanks for contributing solution to sdrta.netematics Stack Exchange!

Please be certain to answer the question. Carry out details and share your research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based on opinion; earlier them up with referrals or an individual experience.

Use sdrta.netJax to style equations. sdrta.netJax reference.

To find out more, see our advice on writing an excellent answers.

See more: How To Be Naked On Imvu - How To Get Naked On Imvu Female 2021 ! New Glitch


Draft saved
Draft discarded

Sign up or log in in


sign up utilizing Google
authorize up making use of Facebook
authorize up making use of Email and Password
send

Post together a guest


surname
email Required, yet never shown


Post together a guest


name
email

Required, however never shown


post Your answer Discard

By clicking “Post her Answer”, friend agree to our terms of service, privacy policy and also cookie policy


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


Upcoming events
Featured on Meta
Linked
1
Is it feasible for a form to have actually equal angles however not equal sides/ vice versa?
2
Action of the symmetry group on polygons
associated
0
Equiangular polygon inscribed in rectangle
13
Is an equilateral triangle the exact same as one equiangular triangle, in any kind of geometry?
2
definition of rectangle
1
present that if a convex pentagon is equilateral, and also two the its nearby inner angles measure 108 degree, then the pentagon is equiangular.
3
all the 2-d polygon that have the right to be used to kind 3-d polyhedrons
5
What is the maximum number of consecutive sides whose lengths girlfriend can select without uniquely determining the polygon?
hot Network inquiries much more hot questions

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


*

sdrta.netematics
company
stack Exchange Network
site architecture / logo © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.9.40693


sdrta.netematics ridge Exchange works best with JavaScript enabled
*

her privacy

By click “Accept all cookies”, you agree ridge Exchange deserve to store cookie on your an equipment and disclose information in accordance v our Cookie Policy.