Lines of Symmetry

Folding Test

You can find if a shape has a Line of Symmetry by folding it.

When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

 

Here I have folded a rectangle one way, and it didn’t work.

symmetry folding no
So this is not a Line of Symmetry

But when I try it this way, it does work (the folded part sits perfectly on top, all edges matching):

symmetry folding yes
So this is a Line of Symmetry

Triangles

A Triangle can have 3, or 1 or no lines of symmetry:

symmetry equilateral triangle symmetry isosceles triangle no symmetry scalene triangle
Equilateral Triangle
(all sides equal,
all angles equal)
Isosceles Triangle
(two sides equal,
two angles equal)
Scalene Triangle
(no sides equal,
no angles equal)
3 Lines of Symmetry 1 Line of Symmetry No Lines of Symmetry

Quadrilaterals

Different types of Quadrilaterals (a 4-sided plane shape):

symmetry square symmetry rectangle symmetry irregular quad
Square
(all sides equal,
all angles 90°)
Rectangle
(opposite sides equal,
all angles 90°)
Irregular
Quadrilateral
4 Lines of Symmetry 2 Lines of Symmetry No Lines of Symmetry

 

symmetry kite symmetry rhombus
Kite Rhombus
(all sides equal length)
1 Line of Symmetry 2 Lines of Symmetry

Regular Polygons

A regular polygon has all sides equal, and all angles equal:

An Equilateral Triangle (3 sides)  has 3 Lines of Symmetrysymmetry equilateral triangle

A Square (4 sides)  has 4 Lines of Symmetrysymmetry square

A Regular Pentagon (5 sides)  has 5 Lines of Symmetrysymmetry regular pentagon

A Regular Hexagon (6 sides)  has 6 Lines of Symmetry

A Regular Heptagon (7 sides)  has 7 Lines of Symmetry

A Regular Octagon (8 sides)  has 8 Lines of Symmetry

And the pattern continues:

  • A regular polygon of 9 sides has 9 Lines of Symmetry
  • A regular polygon of 10 sides has 10 Lines of Symmetry
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