If lines AB, AC, AD and AE are parallel to a line l, then ________ .

Options

A. A, B, C, D and E are collinear points.
B. A, B, C, D and E are non-collinear points.
C. Lines AB and AC are parallel and lines AD and AE are perpendicular.
D. None of these

Answer

To solve the problem, we need to analyze the given information about the lines and their relationships with line l.

### Step-by-Step Solution:

1. **Understanding Parallel Lines**: We are given that lines AB, AC, AD, and AE are all parallel to a line l.

2. **Definition of Parallel Lines**: By definition, if two lines are parallel, they will never meet, no matter how far they are extended.

3. **Transitive Property of Parallel Lines**: If a line is parallel to another line, and a third line is also parallel to the first line, then the third line is also parallel to the second line. This means that if AB is parallel to l, and AC is also parallel to l, then AB is parallel to AC.

4. **Applying the Property**: Since all the lines (AB, AC, AD, and AE) are parallel to line l, we can conclude that:
- AB is parallel to AC
- AB is parallel to AD
- AB is parallel to AE
- AC is parallel to AD
- AC is parallel to AE
- AD is parallel to AE

5. **Conclusion**: Therefore, all lines AB, AC, AD, and AE are parallel to each other.

6. **Co-linear Points**: Since all these lines are parallel, the points A, B, C, D, and E must lie on the same line (which is the line that is parallel to l). Thus, we can conclude that A, B, C, D, and E are co-linear points.

### Final Answer:
If lines AB, AC, AD, and AE are parallel to a line l, then **A, B, C, D, and E are co-linear points**.