The words 'cross', 'intersect', 'cut across', 'oblique', 'diagonal' and 'dissect' can be used as synonyms for the term 'traverse transversely'. All these words depict a movement or action that is perpendicular or diagonal to something else. For instance, one may use the word 'intersect' when talking about two lines that cross path at an angle. Similarly, the term 'dissect' indicates the act of cutting something crosswise, while 'oblique' and 'diagonal' refer to angles or lines that are neither vertical nor horizontal. Therefore, in academic or professional writing, one may use any of these synonyms to add variety and depth to their work.