The question you provided shows two figures where the figure on the right is a scaled copy of the figure on the left. You are asked to identify which side in the figure on the right corresponds to the segment TQ from the left figure, as well as to determine the scale factor.

1. Identifying the Corresponding Side:

   • In the smaller figure on the left, segment TQ is the vertical side of the triangle RTQ.
   • Since the figures are scaled copies of each other, the corresponding side in the larger figure on the right must retain the same relative position.
   • Therefore, the side corresponding to segment TQ in the right figure is LJ, which is the vertical side of the triangle JLK.

2. Determining the Scale Factor:

   • To find the scale factor, we can compare the lengths of corresponding segments in the two figures. The scale factor is the ratio of a side's length in the larger figure to its corresponding side's length in the smaller figure.
   • If we count the units, the length of TQ in the smaller figure is 2 grid units (assuming each square on the grid is 1 unit).
   • The length of LJ in the larger figure is 4 grid units.
   • Thus, the scale factor is $\frac{4}{2} = 2$.

Therefore, the side in the figure on the right that corresponds to segment TQ is LJ, and the scale factor is 2.

Would you like to explore this topic further, or do you have any more questions? Here are some related questions to consider:

1. How does scaling affect the area of similar figures?
2. What happens to the angles of a figure when it is scaled?
3. Can you determine the scale factor by comparing the areas of similar figures?
4. How do you use scale factors in real-world applications, such as maps and models?
5. What are some other properties that remain unchanged under scaling?

Tip: When working with geometric figures on grid paper, counting the grid units can be a quick way to estimate measurements and compare properties like segment lengths and areas.