Problem
Each crease that folds one half exactly onto the other is a line of symmetry, and all of them pass through the centre.
Fourth graders can find a line of symmetry by folding a paper shape and checking that the two halves cover each other — here we just imagine the folds.
4.G.A.3Draw A DiagramFolding smaller shapes: the triangle has 3, the square 4, the pentagon 5 and the hexagon 6.
Smaller shapes are easy to fold and check, so they give me confidence about the rule before I tackle 10 sides.
4.G.A.3Solve An Easier Related ProblemIn every case the number of lines of symmetry equals the number of sides. A regular polygon with n sides has exactly n lines of symmetry.
Each side and each corner lines up with a matching one across the center, so the fold lines come in a neat one-per-side count.
4.G.A.3Look For A PatternA regular polygon with n sides has exactly n lines of symmetry.
A line of symmetry is a crease that lays the shape exactly onto itself, and folding carries every length and angle over unchanged.
Such a crease has to send vertices to vertices, so it runs either through a pair of opposite vertices or through a pair of opposite side midpoints, and those choices come to exactly n.
Each vertex is matched with exactly one vertex across the crease, so the creases can be counted off against the sides one for one.
The decagon takes 5 through opposite corners and 5 through opposite side midpoints: 10.
Because 10 is even, opposite corners pair up and opposite side-midpoints pair up, giving two equal groups of 5 fold lines.
4.G.A.3Draw A DiagramA regular shape has as many lines of symmetry as it has sides — so a 10-sided decagon has 10.