7.02 Regular polygons and symmetry
Regular polygons
Here are some examples of regular polygons.
Now let's take a look at some examples that are not regular polygons, but rather irregular polygons.
Examples
Example 1
Which of these polygons are regular?
A regular polygon has all sides congruent and all angles congruent.
Symmetry
A shape has symmetry if it looks the same before and after a transformation. Symmetries are very common in nature as well as many areas of mathematics.
A line that reflects a shape onto itself is called a line of symmetry.
Exploration
The shape on the left is the original shape. The shape on the right is the same shape folded over the line.
Drag the blue point to move the line. Click 'Next shape' to get a new shape.
- Which shapes had at least one line of symmetry? What similarites do you notice between those shapes?
- Which shapes had no lines of symmetry? What did you notice about those shapes?
- Which shapes had more than two lines of symmetry? What did you notice about those shapes?
For a regular polygon, the number of lines of symmetry is equal to the number of sides.
One way to picture lines of symmetry is with reflections. Another way is to picture folding the shape along a line. Whether reflecting or folding, the resulting shape should perfectly overlap the original.
A shape that has no lines of symmetry is called asymmetric. Neither of these shapes have a line of symmetry.
Examples
Example 2
Use the image below to answer the following:
How many lines of symmetry does this regular polygon have?
Draw the lines of symmetry
A line that reflects a shape onto itself is called a line of symmetry.
Asymmetric shapes are shapes without lines of symmetry.
In a regular polygon, the number of sides is equal to the number of lines of symmetry.