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The task requires identifying a sequence of transformations that maps Figure \( E \) onto Figure \( F \), and then determining if the two figures are congruent.

To start:

### Analysis of Transformations:
1. **Orientation and Position**: 
   - Figure \( E \) appears to be a reflection of Figure \( F \), given that the orientation of the two shapes is reversed.
   - Figure \( E \) is also located below Figure \( F \), so some kind of translation will likely be necessary after reflection.

### Likely Transformation Sequence:
- **Reflection**: Figure \( E \) needs to be reflected across the x-axis to align with the orientation of Figure \( F \). After reflecting, the new shape will be closer to Figure \( F \) but will still be lower on the coordinate plane.
- **Translation**: After the reflection, the figure will need to be shifted up and to the right to match Figure \( F \)'s exact position. This would involve a translation upward along the y-axis and a shift in the positive x-direction.

### Conclusion on Congruence:
- Since the figures undergo rigid transformations (reflection and translation), which do not alter the size or shape of the figures, **the two figures are congruent**.

### Final Answer:
1. The first transformation is **a reflection**.
2. The second transformation is **a translation**.
3. The two figures **are congruent** because **rigid transformations (reflection and translation) are used to map Figure E onto Figure F**.

Would you like a more detailed breakdown of the reflection and translation steps? 

Here are 5 related questions to further explore this concept:
1. What other types of transformations preserve congruence?
2. How do you determine the line of reflection for a given transformation?
3. Can a sequence of rotations replace reflection and translation?
4. What is the effect of a dilation on congruence?
5. How would the transformation differ if the figures were not congruent?

**Tip**: Always verify the orientation after a reflection by checking how corresponding points are aligned.

Use the drop-down menus to state the sequence of transformations that maps Figure E onto Figure F. Then use those transformations to determine: are the two figures congruent? Use the drop-down menus to explain why or why not.

Determine the sequence of transformations (reflection and translation) that maps Figure E onto Figure F. This problem explores key geometry concepts, including rigid transformations and the congruence theorem. Suitable for Grades 8-10.

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