The problem shows two triangles, $\triangle ABC$ and $\triangle FDE$, where triangle $FDE$ is a rotation of triangle $ABC$. The question asks which angle relationships are correct based on the rotation.

Given that $\triangle FDE$ is a rotation of $\triangle ABC$, the corresponding angles of these two triangles should be equal, meaning:

• $\angle F$ corresponds to $\angle B$,
• $\angle D$ corresponds to $\angle A$,
• $\angle E$ corresponds to $\angle C$.

With this information, we can identify the correct statements:

1. $m\angle E = m\angle C$ (Correct: $\angle E$ corresponds to $\angle C$)
2. $m\angle D = m\angle B$ (Incorrect: $\angle D$ corresponds to $\angle A$, not $\angle B$)
3. $m\angle E = m\angle D$ (Incorrect: $\angle E$ corresponds to $\angle C$, and $\angle D$ corresponds to $\angle A$)
4. $m\angle B = m\angle C$ (Incorrect: These angles do not correspond in any triangle)
5. $m\angle D = m\angle C$ (Incorrect: $\angle D$ corresponds to $\angle A$)
6. $m\angle F = m\angle B$ (Correct: $\angle F$ corresponds to $\angle B$)

Thus, the correct statements are:

• $m\angle E = m\angle C$
• $m\angle F = m\angle B$

Would you like more details on these relationships or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the concept of corresponding angles apply to rotated triangles?
2. What properties remain unchanged under a rotation transformation in geometry?
3. Can two triangles be similar but not congruent under rotation? Why or why not?
4. What are the properties of a scalene triangle, and how do they affect rotations?
5. How would you verify if two triangles are congruent through transformations?

Tip: Remember, rotations preserve both the angles and the shape of geometric figures, but not necessarily their orientation.