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In Figure 3, two parallel lines are intersected by a transversal line, creating pairs of corresponding and alternate angles. Here’s how to complete the statements:

1. **Corresponding angles are equal**. Since the parallel lines are intersected by a transversal, the corresponding angles formed are equal.
   
2. **Therefore, alternate angles are also equal**. By the property of parallel lines, when a transversal crosses them, alternate interior angles are equal.

This confirms that **alternate angles are equal when two parallel lines are crossed by another line**.

Would you like further details on this concept?

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Here are some questions to expand on this topic:

1. What is the difference between corresponding angles and alternate interior angles?
2. Why are corresponding and alternate angles equal in parallel lines?
3. How does this property help in solving geometry problems involving parallel lines?
4. Are there other angle pairs that are equal when a transversal crosses parallel lines?
5. How can you prove that alternate angles are equal without using corresponding angles?

**Tip:** Remember that identifying parallel lines and a transversal is crucial to applying angle rules accurately.

Corresponding angles are _____. Therefore, _____.

Explore how corresponding and alternate angles are equal when parallel lines are intersected by a transversal. This concept highlights the Corresponding Angles Postulate and the Alternate Interior Angles Theorem, essential for understanding angle relationships in geometry. Suitable for students in Grades 7-9.

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