An intersection
yeah
the same line
Identical.
Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
Does not lie in
Yes as long as the two lines are intersecting at that point. For example if you looked at an x-y axis, the point (0,0) would lie on both the x and y axis or two different lines.
Two straight lines in the same plane can't possibly have more than one point in common, unless they are both the same line. If they're parallel, they have no common points. If they're not parallel, then have exactly one common point. If they're the same line, then every point on one line is also on the other one.
Because they lie ontop of fault lines.
No. Collinear means on the same line. So collinear points all must lie on the same line. Not parallel lines.
No because only co-linear lines lie on the same plane
collinear plane
A counterexample to the conjecture is when three parallel lines lie in the same plane. In this case, none of the lines intersect at any point, demonstrating that it is possible for three lines in the same plane to not intersect at all. Therefore, the conjecture is proven false.