THEOREM 2.1Line

Intersection Theorem

THEOREM 2.1 If two different lines intersect, their

intersection contains only one point.

As you can see…

In the figure, Line 1 and Line 2 intersect at point P.

Proof: In Line Postulate(3) , two points are contained in one and only one line, therefore, Line 1 and Line 2 cannot intersect in two points but at only one point.

THEOREM 2.2Line-Plane Intersection Theorem

If a line intersects a plane not containing it, then the intersection contains only one point.

Proof: According to the Flat Plane Postulate(6) , if two points of a line lie on a plane, then the line lies on the same plane. Since the line that intersects a plane does not lie on the plane, then only one point of the line is contained in the plane and that is the point of intersection.