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To find the scale factor that takes polygon \( P \) to polygon \( Q \), we can compare the corresponding sides of the two polygons.

### Step 1: Identify corresponding sides
- The side of length 18 in polygon \( P \) corresponds to the side of length 9 in polygon \( Q \).
- The side of length 14 in polygon \( P \) corresponds to the side of length 7 in polygon \( Q \).
- The side of length 8 in polygon \( P \) corresponds to the side of length 4 in polygon \( Q \).

### Step 2: Calculate the scale factor
The scale factor is determined by dividing the length of a side in polygon \( Q \) by the corresponding side in polygon \( P \). 

Using the first pair of corresponding sides:
\[
\text{Scale Factor} = \frac{9}{18} = \frac{1}{2}
\]

You can verify this using the other pairs of corresponding sides:
\[
\frac{7}{14} = \frac{1}{2}
\]
\[
\frac{4}{8} = \frac{1}{2}
\]

### Final Answer
The scale factor that takes polygon \( P \) to polygon \( Q \) is \( \frac{1}{2} \).

Would you like further details or have any questions about this? Here are five related questions to explore:

1. What would be the scale factor from polygon \( Q \) to polygon \( P \)?
2. How does the scale factor affect the area of the polygons?
3. If a third polygon \( R \) has a scale factor of \(\frac{1}{4}\) compared to \( P \), what would the corresponding sides be?
4. How do you find the scale factor if the given sides are not directly proportional?
5. What is the relationship between the perimeters of the two polygons given the scale factor?

**Tip:** Always verify the scale factor with multiple corresponding sides to ensure accuracy, especially when dealing with complex polygons.

What scale factor takes polygon P to polygon Q?

Learn how to find the scale factor between two similar polygons, Polygon P and Polygon Q, by comparing their corresponding side lengths. Understand the geometry concepts involved, including scale factor and similarity theorems. Suitable for students in Grades 6-8.

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