$n$-dimensional affine point-vector space is a pair $\mathbb A^n = \langle \mathbb A, V^n \rangle$, where $\mathbb A$ is an arbitrary set, which elements are called points of affine space, $V^n$ is an $n$-dimensional real vector space together with function $\mathbb A \times \mathbb A \to V^n$, denoted $(A,B)\mapsto \vec{AB}$, such that the following axioms hold:
- $\vec{AB}+\vec{BC} = \vec{AC}$ for any $A,B,C \in \mathbb A$,
- For any $A \in \mathbb A$ and for any $r \in V^n$ there exists a unique $B \in \mathbb A$ such that $\vec{AB} = r$.
In my book it is written that $\mathbb A^3$ is a simpliest model of our physical space (Golubev, Foundations of theoretical mechanics). Then author uses such notions as "two lines are perpendicular". My question is how to introduce a perpendicular in affine space? Hilbert in his Foundations of Geometry introduce a notion of right angle as the angle that is congruent to its complement. Then two lines are perpendicular if their intersection provide us four right angles. What is the way to introduce relation of congruence of angles in affine space then?