CKM unitarity triangle ($V_{ud}{V}_{ub}^{\ast }+V_{cd}{V}_{cb}^{\ast }+V_{td}{V}_{tb}^{\ast }=0$)

Orthogonality of two CKM rows or columns makes the three complex products form a closed triangle. Its area is $|J|/2$, where $J$ is the Jarlskog invariant. Normalizing the displayed column-orthogonality relation gives vertices $0,1,\bar{\rho }+i\bar{\eta }$, with $\bar{\rho }+i\bar{\eta }=-V_{ud}{V}_{ub}^{\ast }/(V_{cd}{V}_{cb}^{\ast })$. A collapsed triangle has zero weak rephasing-invariant CP violation for nondegenerate quark masses.