Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1 + α)- Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.