1. What is the line of symmetry?
A line that cuts a shape into two equal halves is the line of symmetry for that shape.
The line of symmetry is also called the mirror line. Depending on the shape, 2D shapes
can have multiple lines of symmetry.
For the simple arrow shape shown below, it has one line of symmetry in the centre as
shown below.
If you fold the above arrow shape along the dashed line in the centre, both halves would match exactly. So the horizontal line passing through the centre line is the line of symmetry of the above shape.
Here are some shapes with lines of symmetry.
1.1 Some simple 2D Shapes with lines of symmetry
2. Lines of Symmetry for Regular Polygons
Regular polygons: All the regular polygons have lines of symmetry. The number of lines of symmetry for a regular polygon is equal to its number of sides.
Let us look at some of the regular polygons and their lines of symmetry.
2.1 Solved Example
Draw all lines of symmetry on the shape shown below.
Solution: Given shape has 8 equal sides, so it's a regular octagon. For a regular polygon, the number of lines of symmetry is equal to the number of sides. So for a regular octagon, it has 8 lines of symmetry.
2.2 Shapes with no lines of symmetry
Not all shapes have lines of symmetry. Many irregular shapes and Irregular polygons have no lines of symmetry. Let's take a look at a few of these shapes.
Some more examples of irregular shapes with no lines of symmetry.
