Based on the image you provided, we have two quadrilaterals: one on the left with vertices $I, J, H, K$ and one on the right with vertices $U, R, S, T$. The question is asking which side in the figure on the right corresponds to segment $JH$ in the figure on the left, and what the scale factor between the two figures is.

Step 1: Identifying the Corresponding Side

To find the corresponding side to segment $JH$, we need to look for the side in the second figure that matches the relative position of $JH$ in the first figure. Observing the shapes, the relative positions suggest that side $UR$ in the right figure likely corresponds to segment $JH$ in the left figure.

Step 2: Calculating the Scale Factor

The scale factor can be found by measuring the lengths of the corresponding sides in both figures. Let's perform the measurements using the grid units in the image:

• Measure the length of segment $JH$ on the left figure.
• Measure the length of segment $UR$ on the right figure.

The scale factor is calculated as: $\text{Scale Factor} = \frac{\text{Length of } UR}{\text{Length of } JH}$

Let me know if you'd like detailed measurements of these lengths or have any questions!

Follow-Up Questions

1. How do you determine which sides are corresponding in similar figures?
2. What are the properties of scaled figures that help identify corresponding parts?
3. How do you calculate the scale factor when the figure is rotated?
4. Why is understanding the scale factor important in geometry?
5. Can you apply the concept of scale factor to other shapes, like triangles or circles?

Tip: When comparing scaled figures, always check if the angles between corresponding sides are preserved, as this helps confirm their similarity.