Angle relations in triangle

Why does this $$h_z = \begin{cases} -z(L+x) \; , & x\in \left[-L,-z\right]\\ (L-z)x \; , & x\in \left[-z,z\right]\\ z(L-x) \; , & x\in \left[z,L\right] \end{cases}$$ define a $2L$-periodic sawtooth like function with $z \in (0,L)$? In the picture, $L$ is marked as $l$. In the interval $[-z,z]$, for example, I get $\tan(\alpha) = \frac{H}{z}$ with $H$ being the height of the triangle between $0$ and $L$, and $\alpha$ being the angle from the $x$-axis at point $0$ and the triangle. But why is this also equal to $L-z$?