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Using the diagram, classify the angle pairs.



To solve this problem, I'll classify the angle pairs based on the diagram provided.

Given the diagram:

1. **\(\angle 4\) and \(\angle 7\)**:
   - These angles are on the opposite sides of the transversal and are inside the two parallel lines, making them **alternate interior angles**.

2. **\(\angle 2\) and \(\angle 11\)**:
   - These angles are outside the parallel lines and on opposite sides of the transversal, making them **alternate exterior angles**.

3. **\(\angle 6\) and \(\angle 16\)**:
   - These angles are on the same side of the transversal and outside the parallel lines, making them **consecutive exterior angles**.

4. **\(\angle 8\) and \(\angle 13\)**:
   - These angles are corresponding positions on the parallel lines cut by the transversal, making them **corresponding angles**.

5. **\(\angle 1\) and \(\angle 9\)**:
   - These angles are inside the parallel lines and on the same side of the transversal, making them **consecutive interior angles**.

6. **\(\angle 11\) and \(\angle 5\)**:
   - These angles are on the opposite sides of the transversal and outside the parallel lines, making them **alternate exterior angles**.

So, the classifications should be as follows:

1. **Alternate Interior**: \(\angle 4\) and \(\angle 7\)
2. **Alternate Exterior**: \(\angle 2\) and \(\angle 11\)
3. **Consecutive Exterior**: \(\angle 6\) and \(\angle 16\)
4. **Corresponding**: \(\angle 8\) and \(\angle 13\)
5. **Consecutive Interior**: \(\angle 1\) and \(\angle 9\)
6. **Alternate Exterior**: \(\angle 11\) and \(\angle 5\)

Let me know if you want any more details or have questions. 

Here are 5 related questions you might find helpful:

1. How do you identify corresponding angles in a diagram?
2. What are the properties of alternate interior angles?
3. Can consecutive exterior angles ever be equal? Why or why not?
4. How can you prove two lines are parallel using alternate interior angles?
5. What are the conditions for angles to be considered consecutive interior?

**Tip:** When working with transversals and parallel lines, always look for patterns of symmetry to quickly identify angle relationships!

Using the diagram, classify the angle pairs.

Learn how to classify angle pairs formed by parallel lines and a transversal. This problem covers key geometric concepts including alternate interior angles, corresponding angles, consecutive interior angles, and alternate exterior angles. Suitable for students in Grades 8-10.

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