Question

List the alphabets having rotational symmetry and reflection symmetry, and also list the orders in rotational symmetry as well as reflections symmetry.

Answer 1

Identify the alphabets having symmetry:

Alphabets having a reflection symmetry about a vertical mirror are $\mathrm{A},\mathrm{H},\mathrm{I},\mathrm{M},\mathrm{O},\mathrm{T},\mathrm{U},\mathrm{V},\mathrm{W},\mathrm{X},\mathrm{Y}.$

Alphabets having a reflection symmetry about a horizontal mirror are $\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E},\mathrm{H},\mathrm{I},\mathrm{O},\mathrm{X}.$

Alphabets having both horizontal and vertical mirrors are $\mathrm{H},\mathrm{I},\mathrm{O},\mathrm{X}.$

Alphabet having both reflection symmetry as well as rotation symmetry is $\mathrm{O}$

If the alphabets$\mathrm{S},\mathrm{Z},\mathrm{I},\mathrm{H},\mathrm{X},\mathrm{N}$ are rotated by $180°$ degree about particular axes, they remain the same.

Therefore order of $\mathrm{S},\mathrm{Z},\mathrm{I},\mathrm{H},\mathrm{X},\mathrm{N}$ is $2$

Hence, the list of symmetry of alphabets is identified.