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 ShapeFolding it 
 Plane Shape Folding Plane ShapeThe folding Line is Line of Symmetry
 Plane Shape 2 Folding Plane Shape 2The folding Line is NOT Line of Symmetry

Triangle

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

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

Quadrilaterals

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

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

Regular Polygons

3 SidesEquilateral Triangle
Equilateral Triangle
3 Lines of Symmetry 
4 SidesSquare
Square
4 Lines of Symmetry
5 SidesRegular Pentagon
Regular Pentagon
5 Lines of Symmetry
6 SidesRegular Hexagon
Regular Hexagon
6 Lines of Symmetry
7 SidesRegular Heptagon
Regular Heptagon
7 Lines of Symmetry
8 SidesRegular Octagon
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.

Circle

So a Circle has infinite Lines of Symmetry.

Learn More

Irregular Polygon

Consecutive Interior Angles

Angles of Elevation & Depression

Finding an Angle in a Right Angled Triangle

Geometry Index

Leave a Reply

Your email address will not be published. Required fields are marked *

Facebook
Twitter
PINTEREST
LINKEDIN
INSTAGRAM