Step by step
The question
Question: how many lines of symmetry does a regular octagon have?
1 Try the folds
Imagine folding the shape along a line.
If the two halves match exactly, it is a line of symmetry.
Fold through the middles of two opposite sides.
The halves match: line 1.
Fold through two opposite corners.
The halves match: line 2.
Fold through the middles of two opposite sides.
The halves match: line 3.
Fold through two opposite corners.
The halves match: line 4.
Fold through the middles of two opposite sides.
The halves match: line 5.
Fold through two opposite corners.
The halves match: line 6.
Fold through the middles of two opposite sides.
The halves match: line 7.
Fold through two opposite corners.
The halves match: line 8.
2 Count the lines
We found 8.
So a regular octagon has 8 lines of symmetry.
Careful!
Do not stop at the folds through the corners.
The folds through the middles of the sides count too: 8, not 4.
3 Check
Let's check: a regular shape has as many lines of symmetry as sides.
8 sides, 8 lines.
Right!
Let's look back.
First: try the folds.
Then: count the lines.
Last: check.