The image shows two parallel lines $\overrightarrow{DF}$ and $\overrightarrow{GI}$ with a transversal cutting through them. The question asks for alternate interior angles.

Understanding Alternate Interior Angles:

Alternate interior angles are the angles that are:

• On opposite sides of the transversal.
• Between the two parallel lines.
• Non-adjacent.

In this diagram:

• The transversal $\overrightarrow{JH}$ intersects the two parallel lines $\overrightarrow{DF}$ and $\overrightarrow{GI}$.
• $\angle DEH$ and $\angle IHE$ are alternate interior angles, as they meet the above conditions (on opposite sides of the transversal and between the parallel lines).

Correct Answer:

• The correct pair of alternate interior angles is $\angle DEH$ and $\angle IHE$.

Would you like more details or have any questions?

Five related questions:

1. What are corresponding angles in a transversal diagram?
2. How can we identify same-side interior angles?
3. What are alternate exterior angles in this diagram?
4. How can we prove two lines are parallel using angle relationships?
5. Why are alternate interior angles congruent in parallel lines?

Tip:

Remember, alternate interior angles are always congruent if the lines are parallel. This can help you verify your answers!