https://file.aiquickdraw.com/mathbot/file/172727437165344nvoxnj.jpg

The problem asks whether quadrilaterals ABCD and EFGH are congruent and which sequence of transformations maps one onto the other. Let's analyze the situation using the graph.

### Observations:

- **ABCD (Purple Quadrilateral)**: Positioned in the first quadrant.
- **EFGH (Yellow Quadrilateral)**: Positioned in the third quadrant, reflected and rotated from the position of ABCD.

#### Option Analysis:
1. **Translation 2 units left, 5 units down, then 90° clockwise rotation**:
   - Shifting ABCD left and down doesn't seem to align it directly with EFGH.
   
2. **90° counterclockwise rotation, followed by 4 units right and 9 units down**:
   - This transformation doesn't seem to work for aligning both quadrilaterals either.

3. **90° clockwise rotation, followed by 1 unit left and 1 unit down**:
   - This seems plausible. A 90° clockwise rotation could rotate the quadrilateral into a similar orientation as EFGH, and a small translation might align them exactly.

4. **No sequence of transformations maps ABCD onto EFGH**:
   - This would mean no combination of transformations could make the two quadrilaterals congruent, which doesn’t seem correct because the shapes appear to be the same size and shape, just oriented differently.

### Conclusion:
The correct option is likely **option 3**, which involves a 90° clockwise rotation about the origin, followed by a translation of 1 unit left and 1 unit down.

Would you like a detailed breakdown of the transformations involved? Let me know if you have any questions.

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Here are 5 related questions to expand on this concept:

1. How do you determine the direction of rotation for geometric figures?
2. What is the difference between congruence and similarity in geometry?
3. Can you explain how translations and rotations affect the orientation of shapes?
4. What tools can be used to visualize transformations like reflection, rotation, or translation?
5. How do you recognize whether a transformation involves reflection instead of rotation?

**Tip**: When performing transformations, always track the position of each vertex to ensure accuracy!

Are quadrilaterals ABCD and EFGH congruent? If yes, what sequence of transformations maps ABCD onto EFGH?

This problem asks whether quadrilaterals ABCD and EFGH are congruent and which transformations, such as rotations and translations, map one onto the other. Learn the solution involving a 90° clockwise rotation and a translation of 1 unit left and 1 unit down.

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