I can do this trouble by illustration a picture and present of symmetry. Mine question about this trouble is what if that is not an octagon, but any regular polygon. What is a simple way to settle the problem?

Problem: How countless lines of symmetry walk a constant octagon have?


*

I"d say over there is 8 .Drawing an octagon is finest but if you want to do without that , imagine drawing symmetric lines inbetween the currently of the Octagon or you can imagine drawing lines at the suggest where of the 2 currently meet.

You are watching: How many lines of symmetry does a regular octagon have

Lines drawn inbetween currently = 4Lines drawn where 2 points accomplish = 4Total = 8


*

For n-gons over there are constantly $2n$ symmetries in total; $n$ reflections and also $n$ rotations. For this reason in this case there room 16 symmetries in total, 8 reflections and also 8 rotations.

A nice means to think around this is to take into consideration where you can put each vertex. A symmetry is any kind of permutation that preserves adjacency that vertices. Label the vertices 1 through to 8, climate you have actually 8 options for wherein to put the an initial vertex, 2 for the next and also only 1 after that. For this reason we have actually 16 symmetries.

If friend want an ext information on this look up Dihedral groups.


*

My price I got was 10 since if you attract lines threw the octagon due to the fact that it will explain much more to you. - soon grader advice


*

Thanks for contributing an answer to bsci-ch.orgematics ridge Exchange!

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

But avoid …

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

Use bsci-ch.orgJax to format equations. Bsci-ch.orgJax reference.

See more: Convert 200 Kilometers Is How Many Miles Per Hour Are 200 Kilometers Per Hour

To discover more, see our tips on writing an excellent answers.


short article Your answer Discard

By click “Post her Answer”, you agree to our terms of service, privacy policy and cookie policy


How countless different numbers can be created with a continuous polygon the $n$ vertices and a number $d$ of diagonals that this polygon?
How plenty of triangles identified by three vertices that a constant $13$-gon save the polygon's center?
*

site design / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.13.40448


her privacy

By click “Accept all cookies”, friend agree stack Exchange deserve to store cookies on your an equipment and disclose details in accordance v our Cookie Policy.