If two parallel lines are cut by a transversal, then the alternate interior angles are equal

Options

A. TRUE
B. FALSE
C. Cannot be determined
D. None of these

Answer

To demonstrate that if two parallel lines are cut by a transversal, then the alternate interior angles are equal, we can follow these steps:

### Step-by-Step Solution:

1. **Draw Two Parallel Lines**:
- Start by drawing two straight lines that are parallel to each other. Let's label them as line L and line M.

2. **Draw a Transversal**:
- Next, draw a third line that intersects both parallel lines. This line will be called the transversal, and we can label it as line N.

3. **Identify Alternate Interior Angles**:
- When the transversal intersects the parallel lines, it creates several angles. Identify two pairs of alternate interior angles.
- For example, let’s label one pair as angle A and angle B, which are located on opposite sides of the transversal but inside the parallel lines.
- Similarly, label another pair of alternate interior angles as angle C and angle D.

4. **State the Relationship**:
- According to the properties of parallel lines cut by a transversal, we state that angle A is equal to angle B (∠A = ∠B) and angle C is equal to angle D (∠C = ∠D).

5. **Conclusion**:
- Therefore, we conclude that if two parallel lines are cut by a transversal, then the alternate interior angles are equal.