Not necessarily. A rhombus is an equilateral quadrilateral but does not have a line of symmetry. An irregular octagon does not, either.
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An octagon is a 2-dimensional figure, not a line of symmetry. However, it has several lines of symmetry.
A regular octagon has 8 line of symmetry.
Yes.
Yes. Any equilateral shape can have both rotational and line symmetry.
3 of each