Let’s analyze and solve the questions in the image.

1. Vocabulary:

• The diagram shows that line $\ell$ crosses both $p$ and $r$. This makes $\ell$ a transversal.

Answer: Line $\ell$ is a transversal to lines $p$ and $r$.

2. What type of angles are $\angle 1$ and $\angle 2$?

• Referring to the diagram:
  • $\angle 1$ and $\angle 2$ are on opposite sides of the transversal $\ell$ and they are located inside the parallel lines $m$ and $n$.
  • This makes $\angle 1$ and $\angle 2$ alternate interior angles.

Answer: $\angle 1$ and $\angle 2$ are alternate interior angles.

3. Multiple Choice: What type of angles are $\angle 3$ and $\angle 4$?

• Referring to the diagram:
  • $\angle 3$ and $\angle 4$ are on the same side of the transversal $\ell$ and they are located inside the parallel lines $m$ and $n$.
  • This makes $\angle 3$ and $\angle 4$ same-side interior angles.

Answer: $\angle 3$ and $\angle 4$ are D. Same-side interior angles.

Summary of Answers:

1. Transversal
2. Alternate interior angles
3. D. Same-side interior angles

Do you have any questions or want further explanation for any of the concepts?

Here are 5 follow-up questions to extend your understanding:

1. What are the criteria for identifying alternate exterior angles?
2. How can you prove that alternate interior angles are congruent?
3. What happens when the lines $m$ and $n$ are not parallel—are alternate interior angles still congruent?
4. Can a transversal form obtuse angles? Why or why not?
5. How can the relationships between these angles be used in solving for unknown angle measures?

Tip: Always look for parallel lines and the transversal to classify angle types correctly!