Lines of Symmetry of Plane Shapes

Line of Symmetry

Here my dog "Flame" has her face made perfectly symmetrical with a bit of photo magic. The white line down the center is the Line of Symmetry

Folding Test

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

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

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):

So this is a Line of Symmetry

Triangles

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

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):

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

 

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 Symmetry
		A Square (4 sides) has 4 Lines of Symmetry
	A Regular Pentagon (5 sides) has 5 Lines of Symmetry
		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
• ...
• A regular polygon of "n" sides has "n" Lines of Symmetry

Circle A line (drawn at any angle) that goes through its center is a Line of Symmetry. So a Circle has infinite Lines of Symmetry.