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Let’s analyze the problem and identify the corresponding angles, consecutive interior angles, alternate interior angles, and alternate exterior angles based on the diagram.

### Explanation:
In the diagram, we have two sets of parallel lines:
- Line \( EG \) is parallel to line \( AB \).
- Line \( DF \) is parallel to line \( HJ \).

The transversal lines intersecting these parallel lines help us identify angle pairs.

### 25. \( \angle BCG \) and ______ are corresponding angles.
- Corresponding angles are those that lie on the same side of the transversal and in the same relative position.
- \( \angle BCG \) is located on the lower side of the transversal \( CB \).
- The corresponding angle would be \( \angle FCJ \).

**Answer:** \( \angle BCG \) and \( \angle FCJ \) are corresponding angles.

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### 26. \( \angle BCG \) and ______ are consecutive interior angles.
- Consecutive (or same side) interior angles are on the same side of the transversal but inside the parallel lines.
- The consecutive interior angle for \( \angle BCG \) would be \( \angle JCA \).

**Answer:** \( \angle BCG \) and \( \angle JCA \) are consecutive interior angles.

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### 27. \( \angle FCJ \) and ______ are alternate interior angles.
- Alternate interior angles are on opposite sides of the transversal and between the parallel lines.
- For \( \angle FCJ \), the alternate interior angle would be \( \angle BCG \).

**Answer:** \( \angle FCJ \) and \( \angle BCG \) are alternate interior angles.

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### 28. \( \angle FCA \) and ______ are alternate exterior angles.
- Alternate exterior angles are on opposite sides of the transversal but outside the parallel lines.
- For \( \angle FCA \), the alternate exterior angle would be \( \angle BGH \).

**Answer:** \( \angle FCA \) and \( \angle BGH \) are alternate exterior angles.

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### Would you like further details or clarifications?

Here are 5 follow-up questions for further practice:
1. What are the corresponding angles of \( \angle DCF \)?
2. Identify a pair of alternate interior angles involving \( \angle EDC \).
3. What are the consecutive interior angles of \( \angle ACB \)?
4. Find another pair of alternate exterior angles in the diagram.
5. Explain the relationship between corresponding angles and alternate exterior angles in parallel line configurations.

**Tip:** When working with transversals, always remember that parallel lines give rise to predictable angle relationships such as corresponding, alternate interior, and alternate exterior angles!

Complete the statements about corresponding, consecutive interior, alternate interior, and alternate exterior angles based on the given diagram.

Learn how to identify corresponding, consecutive interior, alternate interior, and alternate exterior angles when two parallel lines are crossed by a transversal. This exercise involves applying key theorems like the Corresponding Angles Postulate and Alternate Interior Angles Theorem. Suitable for students in Grades 8-10.

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