Let $l_1$ and $l_2$ be the lines through the origin in $R^2$ that intersect in an angle π/n and let $r_i$ be the reflection about $l_i$. Prove the $r_1$ and $r_2$ generate a dihedral group $D_n$.
So $D_n$ is the dihedral group of order 2n generated by $ρ_θ$, where θ = 2π/n, and a reflection r' about a line l through the origin.
The product $r_1r_2$ of these reflections preserves orientation and is a rotation about the origin. Its angle of rotation is ±2θ.
Could I just say that by the definition of the dihedral group, we need to find a reflection and a rotation which fit the descriptions?