perpendicularity in Euclidean plane

Two lines in the Euclidean plane are perpendicular to each other if and only if they intersect and two of the angles they form are congruent.

This definition on the one in Hilbert’s Grundlagen der Geometrie (“Ein Winkel, welcher einem seiner Nebenwinkel kongruent ist, heißt ein rechter Winkel”).

The perpendicularity of $l$ and $m$ is denoted

$$l\perp m.$$