What if we draw a quadrilateral like this? Does any pair of opposite sides meet if we extend them? Why?

Given is the quadrilateral A B C D . The sides A D and B C are extended to form lines l and m . Here, the lines extended upwards intersect at the point O , as the distance between these two lines is not fixed. Similarly, if the sides A B and C D are extended to form lines r and s , will intersect at the point P as the perpendicular distance between these two lines will keep on decreasing.

Look at the distance between the lines in both figures: What can we say about the distance between two parallel lines?

In the following figure, as we see the perpendicular distance is fixed. i.e., the lines l and m are separated by a fixed distance, so these lines l and m are parallel to each other. Parallel lines never intersect each other. Hence, lines l and m will never meet. Extending to the right sides of the given lines. The given lines r and s , when extended towards the right it intersects at the point O , as the distance between these to lines are not fixed. So, on extending the lines, the lines will intersect each other.