Two parallel lines are cut by a transversal , then which of the following are true ?
1. Pair of alternate interior angles are equal.
2. Pair of corresponding angles are equal
3. Pair of interior angles on the same side of the transversal are supplementary.

Options

A. 1 and 3
B. 1 and 3
C. 1 and 2
D. All of these

Answer

To solve the problem regarding the properties of angles formed when two parallel lines are cut by a transversal, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two parallel lines, let's call them Line A and Line B.
- A transversal line (let's call it Line T) intersects these two parallel lines.

2. **Identifying Angle Types**:
- When Line T intersects Line A and Line B, it creates several angles. We can categorize these angles:
- Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the parallel lines.
- Corresponding Angles: Angles that are in the same position relative to the parallel lines and the transversal.
- Interior Angles on the Same Side of the Transversal: Angles that are on the same side of the transversal and inside the parallel lines.

3. **Evaluating Each Statement**:
- **Statement 1**: "Pair of alternate interior angles are equal."
- This is true. According to the properties of parallel lines cut by a transversal, alternate interior angles are equal.

- **Statement 2**: "Pair of corresponding angles are equal."
- This is also true. Corresponding angles formed by a transversal intersecting parallel lines are equal.

- **Statement 3**: "Pair of interior angles on the same side of the transversal are supplementary."
- This statement is true as well. The interior angles on the same side of the transversal add up to 180 degrees, making them supplementary.

4. **Conclusion**:
- Since all three statements are true, we conclude that the correct answer is that all of these statements are correct.

### Final Answer:
All of the statements are true.