Condition for Straight Lines in Plane to be Parallel/Slope Form/Proof 3

Proof
Let $\psi$ be the angle between $L_1$ and $L_2$

When $L_1$ and $L_2$ are parallel:
 * $\psi = 0$

by definition.

From Angle between Straight Lines in Plane:
 * $\psi = \arctan \dfrac {m_1 - m_2} {1 + m_1 m_2}$

The result follows immediately.