https://file.aiquickdraw.com/mathbot/file/1728332662797e210hqha.jpg

The problem asks us to find the corresponding congruent angles between the two triangles in the diagram.

From the image:

- Triangle \( \triangle ABC \) is on the left.
- Triangle \( \triangle DEF \) is on the right.

When comparing the two triangles, we need to match angles based on their relative positions.

1. Angle \( \angle A \) in \( \triangle ABC \) is at the top left, corresponding to angle \( \angle E \) in \( \triangle DEF \) because they are in the same relative position.
   
2. Angle \( \angle B \) in \( \triangle ABC \) is at the bottom right, corresponding to angle \( \angle F \) in \( \triangle DEF \) as they are both in the same position relative to the other angles.
   
3. Angle \( \angle C \) in \( \triangle ABC \) is at the bottom left, corresponding to angle \( \angle D \) in \( \triangle DEF \) because of their matching locations.

Thus, the correct congruent angles are:
- \( \angle A \cong \angle E \)
- \( \angle B \cong \angle F \)
- \( \angle C \cong \angle D \)

The correct choice is **C**:
\[
\boxed{C. \, \angle A \cong \angle E, \, \angle B \cong \angle F, \, \angle C \cong \angle D}
\]

Would you like more details or explanations on any specific part of this process?

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Here are 5 related questions to expand this concept:
1. How do you determine triangle congruence using side lengths?
2. What are the rules for corresponding parts of congruent triangles?
3. Can you explain how angle-angle (AA) similarity works for triangles?
4. What is the difference between congruent and similar triangles?
5. How do you prove two triangles are congruent using the ASA postulate?

**Tip:** When comparing triangles, always match angles and sides by looking at their relative positions within the figure.

Which choice below shows the corresponding congruence of angles? The triangles are labeled ABC and DEF.

Learn how to find corresponding congruent angles between triangles ABC and DEF. This problem involves understanding relative positions of angles and applying the Angle-Angle (AA) Theorem. Suitable for students in Grades 6-8.

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