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To date at least 10 highly flattened planes of dwarf galaxies are claimed to have been discovered in the Local Universe. The origin of these planes of galaxies remains unknown. One suggestion is that they are related to the large-scale structure of the cosmic web. A recent study found that the normal of a number of these dwarf galaxy planes is very closely aligned with the eigenvector of the shear tensor corresponding to the direction of greatest collapse obtained by reconstructing the full velocity field in the linear regime. Here we extend that work by both considering an additional 5 planes beyond the five examined previously and examining the alignment with respect to the quasi-linear field, a more sophisticated reconstruction, which is a better approximation on smaller (quasi-linear) scales. Our analysis recovers the previous result while not finding a significantly tight alignment with the additional five planes. However, the additional five plane normals also do not appear to be randomly oriented. We conclude that this could be due either to the normals of the new planes being poorly defined and described; the quasi-linear field at those locations being poorly constrained; or different formation mechanisms for the orientation of planes of dwarf galaxies. [ABSTRACT FROM AUTHOR]