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Not necessarily, as two lines can exist in one plane, but they don't always touch each other. An example would be parallel lines, where the lines are parallel to each other. Lines are also not necessarily straight all the time as it can be curvy too, wherein that a straight line or another curvy line that "does" touch the first curvy line could possibly intersect at more than one point.
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What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
Will non parallel lines intersect?
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
Do skew lines intersect if they are in the same plane?
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
When two or more lines intersect at a point they are said to be?
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.
Three lines that intersect in a point but do not all lie in the same plane?
collinear plane
