Product of Slopes of Perpendicular Lines is Minus 1

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Theorem

Let $L_1$ and $L_2$ be straight lines in the plane.

Let $L_1$ and $L_2$ have slopes of $m_1$ and $m_2$ respectively.


Then $L_1$ and $L_2$ are parallel if and only if $m_1 m_2 = -1$.


Proof

This is a special case of Slope of Orthogonal Curves.

$\blacksquare$


Sources