The question asks which angles are alternate interior angles given two parallel lines and a transversal.

Key Concept:

• Alternate interior angles are non-adjacent interior angles that lie on opposite sides of the transversal.
• These angles are congruent when the lines are parallel.

Identifying the Alternate Interior Angles:

• In the diagram:

  • $\overline{BD} \parallel \overline{EG}$, and line $\overline{CFH}$ acts as the transversal.

  • Alternate interior pairs will lie between the parallel lines $BD$ and $EG$, on opposite sides of the transversal $CFH$.

Answer:

• One pair is $\angle EFC$ and $\angle DCF$.
  • These angles are on opposite sides of the transversal $\overline{CFH}$ and between the two parallel lines, which matches the definition of alternate interior angles.

Thus, the correct answer is:

$\angle EFC$ and $\angle DCF$

Do you want further clarification on alternate interior angles or more explanation about why other options are incorrect?

Here are five related questions for practice:

1. What are corresponding angles in parallel lines cut by a transversal?
2. If two alternate interior angles are $65^\circ$, what is the measure of each?
3. What is the relationship between same-side interior angles?
4. How do you prove two lines are parallel using alternate interior angles?
5. Can alternate interior angles be supplementary?

Tip: When dealing with parallel lines and a transversal, visualize the angles between the lines to quickly identify patterns like alternate, corresponding, or co-interior angles.