  We show that loop-induced processes involving new physics particles can
readily satisfy Landau Equation and trigger triangular singularities at high
energy colliders, leading to fully visible Standard Model final states.
Four-particle vertices in new physics allow triangular singularity diagrams to
evade large virtuality suppression. In addition, a $t$-channel triangular
singularity can also occur in particle scattering processes that may extend to
low momentum exchange. We discuss several typical scenarios in supersymmetric
and extended Higgs models, then identify the singular component in the
loop-integral amplitude at specific external momentum points.
