The document discusses two theorems of line and plane geometry. The Line Intersection Theorem states that if two lines intersect, they do so at exactly one point. The Line-Plane Intersection Theorem states that if a line intersects a plane, but is not contained within the plane, their intersection contains only one point. Both theorems are proved using basic postulates about lines and planes in geometry.

1. Line
Intersection
Theorem

2. 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.

3. Line-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.