Theorem (If two lines intersect, then they intersect in exactly one point)

A theorem in Math can be regarded as a statement which is really true and a suitable proof of that fact can also be given.

Statement:
If two lines intersect, then they intersect in exactly one Point.

Proof:
To prove our theorem, we will take help of some of the statements which are already assumed true although they do not have any proof. They are mentioned in the points given below:
 

  1. If we have any two given points, then there can be just one line which passes through them.
  2. If we are given any three points which are regarded as non collinear, then there can be one plane that passes through them.
  3. If there is a line, then it will have two or more than two points.
  4. If there is a plane, then it will have three or more than three non Collinear Points.
  5. Whenever two planes intersect, they intersect by forming a line.
  6. If there are two points in any plane, then this plane will also have the line joining these points.

So from the above given statements it is proved that when two lines intersect, they intersect at only one Point. A line though passes through two or more points but intersects another line at only one point. This point is called the point of Intersection. Hence, there is only one point of intersection for two lines.

Math Topics