One definition of a dihedral group $D_n$ is
$$\langle s,r : s^2=r^2=(sr)^n=1 \rangle.$$
where $s$ is a symmetry along an axis and $r$ is a rotation of $2\pi/n$. I was just thinking this is how dihedral groups are defined but is it possible to show that the dihedral groups can be generated by two generators of order 2?
Rotation by 2*pi/n generates all rotations, so it is left to prove that we can obtain also all symmetries. Check what is $rsr^{-1},r^{2}sr^{-2},r^{3}sr^{-3}$,... up to $r^{n-1}sr^{-(n-1)}$