Final answer:
To prove the given ratio, one would typically demonstrate that triangles SXT and TYU are similar, then use properties of similar triangles to show that SX/XU = TY/YU.
Step-by-step explanation:
The student is asked to prove that the ratios SX/XU and TY/YU are equal in a triangle STU with parallel lines ST and XY. The information provided suggests that this is a geometry problem involving proportional segments in triangles, which can involve concepts such as similar triangles or the intercept theorem (also known as the basic proportionality theorem).
Given that the figures and complete steps of the proof are not provided, a common approach to this proof would involve showing that triangles SXT and TYU are similar by Angle-Side-Angle (ASA) or corresponding angles, then applying the properties of similar triangles to conclude that the pairs of corresponding sides are in proportion, hence SX/XU = TY/YU.
To assist the student further in establishing this proof, it would be necessary to have the diagram or additional information about the relative positions of the points mentioned and any given angles or side lengths.