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Line Intersection Theorem refers to two different lines intersecting in at most one point.
In projective geometry, an intersection theorem or incidence theorem is an incidence structure consisting of points, lines, and possibly higher-dimensional objects and their incidences, together with a pair of non-incident objects A and B (for instance, a point and a line).
The basic premise of the theorem is that, whenever a set of objects satisfies the incidences (i.e. can be matched up with the objects of the incidence structure in a way that preserves incidence), then the objects corresponding to A and B must also be incident. An intersection theorem is not necessarily true in all projective geometries; it is rather a property which some geometry satisfy but not others.
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