Fashion rulers represent smooth sew-able lines to help guide pattern alterations. In this diagram, a pants pattern is being adjusted along the side and waist seam with a curved ruler.
The ruler provides us with more than just a convenient template edge. The tick marks on the ruler guide us so that the edges from different pattern pieces can flow together when sewn.
Using the tick marks ensures that not only the side seam is adjusted appropriately after fitting, but that the waistline seam will flow from front to back.