Question

If lines AB, AC, AD and AE are parallel to a line l, what can be said about the points A, B, C, D and E?

Answer 1

Hint: We know that if two or more lines are parallel to a given line then all the lines are parallel to each other. Also, we know that we can draw only one line parallel to the given line from a single point.

Complete step-by-step answer:
In the given question, we have been given that the lines AB, AC, AD, and AE are parallel to line l. As we know that if two or more lines are parallel to a given line then all the lines are parallel to each other. AB, AC, AD, and AE are also parallel to each other having point A as common to each line.
Now, we also know that there is only one line that can be drawn parallel to the given line from a point not on the line. All the points A, B, C, D, and E will lie on one line as shown below.

Hence, the points A, B, C, D, and E are collinear points.

Note: The statement is said that there is only one line that can be drawn parallel to the given line from a point not on the line. This is known as Parallel Play Fair’s Axiom. Also, collinear points are the points that lie on the same line.