Symmetry can be found in nature, art, and in architecture. Line of symmetry is also known as line of reflection, and if two sides match each other they are congruent. Line of symmetry is the imaginary line where you fold the image and have both halves match exactly. The two images will be mirror image to each other.

For example, butterfly is symmetrical.

To know if a shape has line of symmetry consider folding it and if the folded part sits perfectly on top (all edges matching) then the fold line is said to have a line of symmetry.  Line of symmetry can be found by drawing a line horizontally, vertically or diagonally and if they are not mirror images then it said to have no line of symmetry.

Given below are the different types of line symmetry.

Zero line of Symmetry
For certain shapes there will be no line of symmetry whether you wish to find it vertically, horizontally or diagonally.

                  Scalene triangle - No angles will be equal.
Symmetry Scalene Triangle

One Line of Symmetry

All shapes with at least one line of symmetry will be symmetrical.
Example: Isosceles triangle -  Two sides will be equal, Isosceles trapezoid.
Symmetry Isosceles Triangle

Infinite lines of symmetry
A line that goes through its center will be the line of symmetry. Whole xy -coordinate will have infinite lines of symmetry.
Example: Circle
Circle Symmetry
In a rectangle opposites sides will be equal and all angles will be 90$^{0}$ so there will be two lines of symmetry.
Symmetry Rectangle
In a square all sides will be equal and all angles will be $90^{0}$. So a square will have four lines of symmetry.
Symmetry Square
A triangle might have one, three or no lines of symmetry.

Equilateral triangle - All sides as well as all angles will be equal. There will be three lines of symmetry.

Symmetry Equilateral Triangle
Isosceles triangle - Two sides will be equal. Line of symmetry will be 1.

Scalene triangle - No sides and no angles will be equal so no line of symmetry.
A  regular hexagon will have six lines of symmetry. Hexagon contain 6 edges and six vertices.
Symmetry Regular Hexagon
A regular octagon will have 8 lines of symmetry as it has 8 sides.
Symmetry Regular Octagon