On the properties of Dihedral group

Question

Let $G=D_{2n}$ be a dihedral group of order $2n$, where $n$ is even. We know in this case $|Z(D_{2n})|=2$. I need an idea for a proof of the fact $D_{2n}/Z(D_{2n}) \cong D_n$.

Answer 1

If your group is generated by a rotation $\sigma$ and a reflection $\tau$, the homomorphism that maps $\sigma$ to $\sigma^2$ and fixes $\tau$ has kernel $Z$ and the required image.