In the picture below, ∠1
and ∠13
are corresponding angles.

Two horizontal parallel lines l and m are intersected by two parallel transversals, a and b. The top left to bottom left angles in the clockwise direction formed by the intersection of line l with line a are labeled 1, 8, 7, and 2. The top left to bottom left angles in the clockwise direction formed by the intersection of line l with line b are labeled 9, 12, 11, and 10. The top left to bottom left angles in the clockwise direction formed by the intersection of line m with line a are labeled 3, 6, 5, and 4. The top left to bottom left angles in the clockwise direction formed by the intersection of line m with line b are labeled 13, 14, 15, and 16.
Question 4Select one:
True
False

To determine whether the statement "∠1 and ∠13 are corresponding angles" is true or false, we need to analyze the configuration of lines and angles described.

**Corresponding angles** are angles that are in the same position at each intersection where a transversal crosses two parallel lines.

Given the description:
- We have two horizontal parallel lines \( l \) and \( m \).
- These lines are intersected by two parallel transversals \( a \) and \( b \).

From the description of angles:
- \( \angle 1 \) is formed at the intersection of line \( l \) and transversal \( a \).
- \( \angle 13 \) is formed at the intersection of line \( m \) and transversal \( b \).

Since \( \angle 1 \) and \( \angle 13 \) are located at different intersections (with different transversals), they **cannot** be corresponding angles. Corresponding angles occur at the same transversal with parallel lines. 

Therefore, the statement that "∠1 and ∠13 are corresponding angles" is **false**.

### Would you like further details on corresponding angles or have any questions?

### Related Questions:
1. What are alternate interior angles?
2. How can you identify corresponding angles?
3. What is the relationship between alternate exterior angles?
4. Can corresponding angles be equal if the transversals are not parallel?
5. How do parallel transversals affect angle relationships?
6. What are co-interior angles?
7. How do you prove that two lines are parallel using angles?
8. What role do vertical angles play in this setup?

**Tip:** When identifying corresponding angles, always look for angles that occupy the same relative position at different intersections made by the transversal with parallel lines.

Explore the concept of corresponding angles in geometry with a focus on parallel lines intersected by transversals. Determine whether ∠1 and ∠13 are corresponding angles through detailed analysis. Suitable for Grades 7-9.

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