I'm sorry if this is an extremely simple question, but I'm honestly having a hard time understanding a theorem in my geometry book. Here is the theorem:
"If two lines intersect, then exactly one plane contains the lines."
Now, each line contains two points, and according to another theorem in my book:
"If two lines intersect, then they intersect in exactly one point."
and three noncollinear points define a plane.
Now, a line endlessly continues in two opposite directions, if two lines were to intersect, shouldn’t that create $5$ points? And I'm also wondering if that would create two different planes (with both planes sharing one point at the intersection.)