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

Let's consider corresponding sides:
- One pair of corresponding sides is \( 8 \) (polygon \( P \)) and \( 4 \) (polygon \( Q \)).
- Another pair is \( 18 \) (polygon \( P \)) and \( 9 \) (polygon \( Q \)).
- The third pair is \( 14 \) (polygon \( P \)) and \( 7 \) (polygon \( Q \)).

To find the scale factor, we divide the length of a side in polygon \( Q \) by the length of the corresponding side in polygon \( P \).

\[
\text{Scale factor} = \frac{4}{8} = \frac{9}{18} = \frac{7}{14} = \frac{1}{2}
\]

Thus, the scale factor from polygon \( P \) to polygon \( Q \) is \( \frac{1}{2} \).

Would you like more details on this or have any questions?

Here are some related questions:
1. What would the scale factor be if polygon \( Q \) were larger than polygon \( P \)?
2. How do you determine if two polygons are similar?
3. What happens to the area of a polygon when scaled by a factor of \( \frac{1}{2} \)?
4. Can a polygon be a scaled copy if one angle measurement is different?
5. How can you find the scale factor using the perimeter of two similar polygons?

**Tip:** Always compare corresponding sides when finding a scale factor between similar figures.

What scale factor takes polygon P to polygon Q?

Learn how to find the scale factor between similar polygons P and Q by comparing corresponding side lengths. This example covers key concepts such as proportions and scale factors, making it ideal for students in Grades 6-8.

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