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

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

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

When $L_1$ and $L_2$ are perpendicular:
 * $\psi = \dfrac \pi 2$

by definition.

From Tangent of Right Angle $\tan \dfrac \pi 2$ is undefined.

This happens $1 + m_1 m_2 = 0$.

The result follows.