Methods for separating glass sheets from glass ribbons are disclosed. One method includes forming a glass ribbon having a curvature in a lateral direction. A conformable nosing is engaged with a first surface of the glass ribbon such that the conformable nosing conforms to the curvature of the glass ribbon. The glass ribbon is scored along a scoring line on a second surface of the glass ribbon. The conformable nosing is then at least partially disengaged from the first surface of the glass ribbon by adjusting a bow of the conformable nosing. A bending moment is applied to the glass ribbon to separate a glass sheet from the glass ribbon at the scoring line. Application of the bending moment conforms the curvature of the glass ribbon to the bow of the conformable nosing prior to the glass sheet separating from the glass ribbon.