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We are given two parallelograms, \( ABCD \) and \( EFGH \), where \( EFGH \) is a dilation of \( ABCD \). The dilation factor is the ratio between corresponding sides of the two parallelograms.

From the image:
- In parallelogram \( ABCD \), side \( AB \) = 4 units and side \( AD \) = 2 units.
- In parallelogram \( EFGH \), side \( EF \) = 12 units and side \( EH \) = 6 units.

To find the scale factor \( k \), we compare the lengths of corresponding sides. Using side \( AB \) and side \( EF \):
\[
k = \frac{EF}{AB} = \frac{12}{4} = 3.
\]
Thus, the scale factor \( k = 3 \).

The correct answer is \( k = 3 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you determine corresponding sides in a dilation problem?
2. What happens to the angles during a dilation?
3. Can the scale factor in a dilation be negative?
4. How do you find the area of a figure after dilation?
5. How does dilation affect the perimeter of a figure?

**Tip**: Always verify the scale factor using multiple pairs of corresponding sides when possible to ensure accuracy.

What is the scale factor between parallelogram ABCD and its dilation EFGH?

Learn how to determine the scale factor in a dilation problem with parallelograms. In this example, parallelogram ABCD is dilated to EFGH, and we find the scale factor by comparing corresponding sides. This is an essential concept in Geometry, suitable for Grades 8-10.

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