Question

Analyze the reflectional symmetry of the regular polygons. The square has -fold reflectional symmetry. The regular octagon has -fold reflectional symmetry.

Answer 1

The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.

Explanation:

For a square,

There are two lines of symmetry along two diagonals and

two lines of symmetry along midpoints of two pairs of opposite sides.

Therefore, there are 4 lines of reflectional symmetry in total.

For a regular octagon,

There are four lines of symmetry along four diagonals and

four lines of symmetry along midpoints of four pairs of opposite sides.

Therefore, there are 8 lines of reflectional symmetry in total.