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?

geometry

re-publishing

cite

follow

asked january 1 "12 at 23:41

Peter OlsonPeter Olson

2,16511 yellow badge2020 silver badges3737 bronze title

$endgroup$

2

include a comment |

## 2 answer 2

active earliest Votes

9

$egingroup$

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.

share

cite

monitor

answered jan 1 "12 at 23:47

TonyKTonyK

57.8k44 gold badges7575 silver badges162162 bronze badges

$endgroup$

2

include a comment |

1

$egingroup$

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.

re-publishing

point out

monitor

answered jan 1 "12 in ~ 23:48

hmakholm left end Monicahmakholm left over Monica

273k2222 yellow badges391391 silver badges646646 bronze title

$endgroup$

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* …

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

send

### Post together a guest

name

email Required, but never shown

### Post together a guest

surname

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

Linked

1

Is it possible for a form to have actually equal angles yet not same sides/ evil versa?

2

Action that the symmetry team on polygons

related

0

Equiangular polygon inscriptions in rectangle

13

Is an equilateral triangle the very same as an equiangular triangle, in any type of geometry?

2

meaning of rectangle

1

present that if a convex pentagon is equilateral, and also two of its nearby inner angles measure 108 degree, then the pentagon is equiangular.

3

all the 2-d polygon that have the right to be offered to kind 3-d polyhedrons

5

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.

betterworld2016.org

firm

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.