Definition:
Imaginary lines that create equal parts of a figure, or geometrical object. When the object is divided by this line (the as if you would fold it), the two parts would match perfectly at each point; thus creating a symmetrical image.

Symmetrical forms are found throughout our world—in nature, man-made objects, and many creative forms of artwork. Being able to see symmetry can help bring together visual elements and give an overall impression of balance and beauty within the same image.

Examples of Symmetrical Shapes

Shape	Number of Lines of Symmetry	Explanation
Square	4	Two vertical, two horizontal, and two diagonal lines.
Rectangle	2	One vertical and one horizontal line (if not a square).
Equilateral Triangle	3	One line from each vertex to the midpoint of the opposite side.
Isosceles Triangle	1	Only one line from the apex to the midpoint of the base.
Circle	Infinite	Any line passing through the center is a line of symmetry.
Regular Pentagon	5	Five lines (one from each vertex to the midpoint of the opposite side).
Rhombus	2	Two diagonal lines (connecting opposite corners).
Kite	1	Only one vertical line (along the longest diagonal).

Steps for Identifying Lines of Symmetry:

1) Visually Analyse: If you folded this object on the line, would it match perfectly? If so, this is a line of symmetry.
2) Use a Mirror: Cover the line with a mirror; if everything on the other side of the line appears, it has a twofold look.
3) Count Equal Sides and Angles: Regular polygons (with equal sides/angles) have several lines of symmetry. An irregularly shaped object may have no lines of symmetry.

Drawing Lines of Symmetry

How to Create Symmetry Lines

Fold the Shape mentally:
Visualise the fold and locate the split.
Draw a straight edge:
Using the straight edge, draw along the fold to create the symmetry line.
Verify:
Ensure that both sides of the symmetry line are identical (i.e., mirrors).

Example Shapes

– Rectangle:
Draw one vertical symmetry line and one horizontal symmetry line through the center of the rectangle.
– Circle:
You can draw any number of symmetry lines as long as they pass through the centre of the circle.
– Isosceles Triangle:
Draw a symmetry line from the top vertex of the triangle to the midpoint of the triangle’s base.

Count Lines of Symmetry

What is a Line of Symmetry?

An axis of symmetry (also known as a line of symmetry) is an imaginary line along which a shape can be divided into two equal or identical halves. One half is the “mirror” view of the other half.

Important information about axes of symmetry:

– If you were to fold a shape along a symmetry line and both halves of the shape fit perfectly together, then that fold would be considered a symmetry line.
– Some shapes can have multiple symmetry lines, while others may have none.
– Regular polygons (regular shapes) always have the same number of axes of symmetry as they do sides.

Examples: Counting Lines of Symmetry

Shape	Number of Lines of Symmetry	Explanation
Square	4	– 2 vertical & horizontal lines

• 2 lines- diagonally.
• Circle- Infinite total; any line that goes directly through the centre is a symmetry line.
• Regular pentagon- 5 total; each vertex has a line that connects it to the midpoint of the opposite side.
• Equilateral triangle- 3 total; each vertex has an axis of symmetry to the opposite side of the triangle.
• Rectangle (not a square)- 2 total; only vertical and horizontal centre lines are symmetry lines.
• Isosceles triangle- 1 total; the apex of the triangle has one line of symmetry to the midpoint of the base.
• Rhombus- 2 total; both diagonals are axes of symmetry.
• Regular hexagon- 6 total; 3 diagonal symmetry lines pass through opposite vertices.
• 3 lines running through the midpoints of opposite sides,
• Scalene triangle- 0 axes of symmetry; no equal sides or angles means that there are no axes of symmetry.

Exercises: Practice Counting Symmetry Lines

Exercise 1: Basic Shapes

Find the number of axes of symmetry in the following shapes:
Heart,
Letter H,
Star (five pointed),
Octagon (stop sign).

Exercise 2: Physical Objects

Find lines of symmetry for:
Your soccer ball which is made up of pentagons and hexagons.
Your snowflake has 6-fold symmetry
The wings of a butterfly.

Exercise 3: Draw It and Count It

Draw a regular heptagon (which has 7 sides) and count how many lines of symmetry it has.
Draw a kite shape and check if it has line symmetry along a vertical axis or horizontally, and if it has either diagonal symmetry.
Cut a notch into one side of a rectangle; does the rectangle have any lines of symmetry anymore?