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.