Abstract
Entanglement is one of the important resources in quantum tasks. Recently, Yang et al. [arXiv:2205.08801] proposed an entanglement polygon inequalities (EPI) in terms of some entanglement measures for n-qudit pure states. Here we continue to consider the entanglement polygon inequalities. Specifially, we show that the EPI is valid for n-qudit pure states in terms of geometric entanglement measure (GEM), then we study the residual entanglement in terms of GEM for pure states in three-qubit systems. At last, we present counterexamples showing that the EPI is invalid for higher dimensional systems in terms of negativity, we also present a class of states beyond qubits satisfy the EPI in terms of negativity.