In recent years, it has become clear that color-ordered scattering amplitudes in various theories can be encoded as logarithmic differential forms on particular geometries, called positive geometries. In particular, tree-level amplitudes in maximally supersymmetric Yang-Mills theory in spinor helicity space are governed by the momentum amplituhedron. Due to the group-theoretic structure underlying color decompositions, color-ordered amplitudes enjoy various identities which relate different orderings. In this talk, after a review of the basics of positive geometries and of the momentum amplituhedron, I will show how the Kleiss-Kuijf relations arise geometrically in this framework.