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The problem involves describing a sequence of transformations that map pentagon HIJKL onto pentagon CDEFG, showing that they are similar.

### Analysis:
- **Pentagon HIJKL** is larger and positioned in the first quadrant.
- **Pentagon CDEFG** is smaller and positioned in the fourth quadrant.

### Steps to Map HIJKL to CDEFG:
1. **Rotation**: The problem states to rotate pentagon HIJKL counterclockwise about the origin. To align HIJKL with CDEFG, we would likely need to rotate by **180 degrees**.

2. **Dilation**: After rotation, pentagon HIJKL needs to be scaled down to match the size of pentagon CDEFG. The appropriate scale factor can be calculated by comparing corresponding sides of HIJKL and CDEFG. By observing the sides in the diagram, the scale factor appears to be **\(\frac{1}{2}\)**.

### Final Answer:
- **Rotation**: Rotate HIJKL counterclockwise by **180 degrees** about the origin.
- **Dilation**: Then, dilate with respect to the origin by a scale factor of **\(\frac{1}{2}\)**.

This transformation sequence will map HIJKL onto CDEFG, demonstrating that the two pentagons are similar.

Would you like a more detailed explanation, or do you have any specific questions? Here are some related questions you might find interesting:

1. How do you determine the appropriate rotation angle for mapping one shape onto another?
2. What is the significance of the scale factor in proving similarity between polygons?
3. How can you verify that two polygons are similar after applying a sequence of transformations?
4. Can reflection also be used in addition to rotation and dilation to map polygons onto each other?
5. What are some examples of transformations that preserve the size and shape of a figure?

**Tip:** When working with transformations, always consider the order of operations (rotation, reflection, translation, dilation) as it can impact the final result.

Complete the paragraph to describe a sequence of transformations that show the pentagons are similar: First, rotate HIJKL counterclockwise about the origin. Then, dilate it with respect to the origin by a scale factor of ____.

Understand how to map pentagon HIJKL onto pentagon CDEFG using geometric transformations. Learn about rotation and dilation transformations to prove similarity between two polygons. Suitable for students in Grades 8-10.

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