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In the image provided, the lines \(t\) and \(g\) are intersected by the transversal \(r\). Angle 1 (\(\angle 1\)) and angle 3 (\(\angle 3\)) are located on opposite sides of the transversal \(r\) and are inside the space between the lines \(t\) and \(g\), making them alternate interior angles.

The property of alternate interior angles states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. Therefore, \(\angle 1\) and \(\angle 3\) are congruent because they are alternate interior angles.

Would you like more details on this topic or have any other questions?

Here are some follow-up questions you might consider:
1. What happens to the angle measurements if line \(t\) is not parallel to line \(g\)?
2. How can you prove that two lines are parallel using the concept of corresponding angles?
3. What are same-side interior angles, and what is their relationship when the lines are parallel?
4. What is the significance of vertical angles in geometry?
5. Can alternate exterior angles also be used to determine the parallel nature of two lines?

**Tip:** To strengthen your understanding of angle relationships, practice identifying different types of angles in various intersecting line diagrams and consider how their properties change if the lines are not parallel.

∠1 and ∠3 are congruent because they are ________________.

This problem helps students understand why ∠1 and ∠3 are congruent using the Alternate Interior Angles Theorem. The problem involves a transversal intersecting two lines, demonstrating the congruency of alternate interior angles. Suitable for students in Grades 6-8.

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