Theorem 2.1 and 2.2
Download as pptx, pdf1 like791 views
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.
Theorem 2.1 and 2.2
- 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.