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.

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.

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.

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.

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!