Lines of Symmetry of Plane Shapes

The line of symmetry is the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves.

How to find a shape has a Line of Symmetry ?

1. You can find a shape has a Line of Symmetry or not by folding it
2. When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.

Examples

 Plane Shape Folding it The folding Line is Line of Symmetry The folding Line is NOT Line of Symmetry

Triangle

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

 Equilateral Triangle(all sides equal, all angles equal) 3 Lines of Symmetry Isosceles Triangle(2 sides equal, 2 angles equal) 1 Line of Symmetry Scalene Triangle(no sides equal, no angles equal) no Line of Symmetry

A Quadrilateral 4, 2, or 1 or no lines of symmetry:

 Square(all sides equal, all angles 90°) 4 Lines of Symmetry Rectangle(opposite sides equal, all angles 90°) 2 Lines of Symmetry Rhombus(all sides equal length) 2 Lines of Symmetry Kite 1 Line of Symmetry Irregular Quadrilateral no Line of Symmetry

Regular Polygons

 3 Sides Equilateral Triangle 3 Lines of Symmetry 4 Sides Square 4 Lines of Symmetry 5 Sides Regular Pentagon 5 Lines of Symmetry 6 Sides Regular Hexagon 6 Lines of Symmetry 7 Sides Regular Heptagon 7 Lines of Symmetry 8 Sides Regular Octagon 8 Lines of Symmetry

And the pattern continues:

A regular polygon with 9 sides has 9 Lines of Symmetry

A regular polygon with 10 sides has 10 Lines of Symmetry

A regular polygon with “n” sides has “n” Lines of Symmetry

Circle

Any line that goes through its center is a Line of Symmetry.

So a Circle has infinite Lines of Symmetry.