Two parallel lines meet each other at some point.
Think of two lines, say \(l\) and \(m\).
We say they are parallel when:
\(l \parallel m\)
This means:
By definition of parallel lines:
\(\text{Parallel lines never meet.}\)
Suppose they meet at a point \(P\).
Then \(P\) lies on both \(l\) and \(m\).
This would mean \(l\) and \(m\) intersect.
But intersecting lines are not parallel.
This is a contradiction.
So, the statement “Two parallel lines meet each other at some point” is false.