1. The problem asks why the ratio $\frac{BC}{DE}$ is proportional in step 3. 2. Typically, this proportionality arises from the properties of similar triangles or parallel lines intersecting transversals. 3. If $BC$ and $DE$ are segments on two lines cut by parallel lines, then by the Basic Proportionality Theorem (Thales' theorem), the segments are proportional. 4. The theorem states: If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. 5. Therefore, $\frac{BC}{DE} = \frac{AB}{AD}$ or a similar ratio depending on the figure. 6. This proportionality is fundamental in geometry and is used to establish equality of ratios between corresponding segments. 7. Hence, $\frac{BC}{DE}$ is proportional because the segments lie between parallel lines or within similar triangles, ensuring their lengths maintain a constant ratio.