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.
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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
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