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The image shows a question asking to identify which figures represent congruent angles in a series of diagrams with intersecting lines. Let's walk through how to solve the problem.

To check for congruent angles, we look for pairs of angles that:
1. Are **vertical angles** (formed by two intersecting lines, directly across from each other).
2. Are **corresponding angles** (formed when a transversal crosses two parallel lines, located in the same relative position at each intersection).
3. Are **alternate interior angles** (inside two parallel lines, on opposite sides of the transversal).

Here's a breakdown of each figure:
- **A**: The two marked angles are on opposite sides of the transversal but not inside parallel lines, so they are not congruent.
- **B**: The angles are vertical angles, which are congruent.
- **C**: The angles are alternate interior angles, which are congruent.
- **D**: The angles are vertical angles, which are congruent.
- **E**: The angles do not fit any of the rules for congruent angles.
- **F**: The angles are corresponding angles, which are congruent.

Thus, the correct answers are **B, C, D, and F**.

Would you like further clarification, or have any questions? Here are some related questions to expand on the concept:

1. What are the characteristics of corresponding angles in parallel lines?
2. How do alternate exterior angles behave when two parallel lines are cut by a transversal?
3. Why are vertical angles always congruent?
4. How can you prove that alternate interior angles are congruent in a geometric proof?
5. Can congruent angles also be supplementary? Under what conditions?

**Tip**: When solving for congruent angles, look for patterns like "Z" shapes (for alternate interior angles) or intersecting lines (for vertical angles).

In which figures are the marked angles congruent? Select all the correct answers.

Learn how to identify congruent angles in figures with parallel lines and transversals. This worksheet problem explores vertical angles, corresponding angles, and alternate interior angles, helping students understand key geometric theorems. Suitable for Grades 8-10.

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