Lines Of Symmetry Of Plane Shapes - Math Is Fun

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Lines of Symmetry of Plane Shapes

Line of Symmetry

dog mirror

Here my dog "Flame" has her face made perfectly symmetrical with some photo editing.

The white line down the center is the Line of Symmetry

Read more at Reflection Symmetry.

Folding Test

We can find any lines of symmetry in a shape by folding it.

When the folded part sits perfectly on top, with all edges matching, that 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:

symmetry equilateral triangle An Equilateral Triangle (3 sides) has 3 Lines of Symmetry symmetry square A Square (4 sides) has 4 Lines of Symmetry symmetry regular pentagon A Regular Pentagon (5 sides) has 5 Lines of Symmetry symmetry regular hexagon A Regular Hexagon (6 sides) has 6 Lines of Symmetry symmetry regular septagon A Regular Heptagon (7 sides) has 7 Lines of Symmetry symmetry regular octagon 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

circle symmetry

A line (drawn at any angle) that goes through its center is a Line of Symmetry.

So a Circle has infinite Lines of Symmetry.

2509, 2510, 9003, 9004, 9005, 793, 9165, 9167, 9166, 498 Reflection Symmetry Symmetry Geometry Index

Tag » How Many Lines Of Symmetry Does An Equilateral Triangle Have