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Plane Geometry contains all shapes like lines, triangles and Circles. Planes are basically shapes which we can draw on a flat surface. Plane is two dimensional forms which contains points and line segments. We can say that plane is flat surface without thickness.

Plane is defined as the Set of infinite points which have four sides with infinite length and infinite width. And all these points are connected to make a plane. Plane contains draw through points and line segments. To draw plane on paper we have to follow some rules which are follows:
  1. First draw the x-scale on a paper with perfect parameters.
  2. Then draw the y-scale on a paper with perfect parameters.
  3. After that we take given points. Let’s assume we have x-axis points x1, x2, x3, x4 and y-axis points y1, y2, y3, y4.
  4. Now we place all these points on ‘x-y’ axis according to its dimension and direction.
  5. Finally connect the pairs of two points to create line segments. When all line segments are connected to each other we find a plane.
  6. The resulting plane is x-y plane.

To understand more deeply about the plane, we consider an example of a plane where we have four points A(1,5), B(5,5), C(3,2), D(6,2).
Plane


Theorem (If Two Lines Intersect, then Exactly One Plane contains both Lines)

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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 exactly one plane contains both lines.

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 a plane contains the both the Intersecting Lines. When two lines intersect they intersect at a Point called the point of Intersection. If a plane contains a line, then it also contains the point of intersection. The point of intersection is common point for both the lines. So, a plane contains both the lines which intersect each other.