Alternate interior angles between parallel lines are equal

Answer

### Step-by-Step Solution:

1. **Identify the Parallel Lines and Transversal**:
- We have two parallel lines, which we will label as Line L and Line M.
- A transversal line, which we will label as Line P, intersects both parallel lines.

2. **Label the Angles**:
- When the transversal intersects the parallel lines, it creates four angles.
- We will label these angles as Angle 1, Angle 2, Angle 3, and Angle 4.

3. **Identify Alternate Interior Angles**:
- Alternate interior angles are the pairs of angles that lie between the two parallel lines but on opposite sides of the transversal.
- In this case, Angle 1 and Angle 2 are one pair of alternate interior angles, and Angle 3 and Angle 4 are another pair.

4. **State the Equality of Alternate Interior Angles**:
- According to the property of alternate interior angles, we can state that:
- Angle 1 = Angle 2 (since they are alternate interior angles)
- Angle 3 = Angle 4 (since they are also alternate interior angles)

5. **Conclusion**:
- Therefore, we conclude that alternate interior angles formed by a transversal intersecting two parallel lines are equal.