Geometry is one of the ancient branches of mathematics which deals with the properties and construction of figures that is of solids, surfaces and lines. Plane Geometry deals only with the line and plane (or flat surface). The Science of Geometry is deductive, certain common notions being assumed, to lead necessarily to further results. These common notions are called axioms. Hence understanding geometry requires only a small number of simple fundamental principles known as axioms of geometry.

Some basic definitions:

Line:

A Line is length without breadth or thickness. The Extremities of a Line are called points: and any place between the extremities is also called a point.

Straight Line:

Straight line is join of two points covering minimum distance. A straight line can also be defined as intersection of two non-parallel planes. A line segment is a line of fixed length or a line with a beginning and with an end.

Curved Line:

A Curved Line is one which changes its direction at every point. Thus, ABC is a curve line.

Parallel Lines:

Two straight lines in the same plane, if the distance between them is always constant or the lines having same directions are said to be parallel lines. Parallel lines do not intersect.

Perpendicular Lines:

Two lines that intersect each other at right angles are said to be perpendicular, in the given diagram line \(x\) is perpendicular to the line \(y\).

Plane:

Plane is a surface such that the join of any two points on this surface wholly lies on the surface. in simple words plane is a flat surface. Intersection of two planes results in a line as shown in the diagram.

Some Important Facts:

1. All lines passing through a given point are known as concurrent lines. There can be infinite such lines for a given point.
2. If two lines in the same plane are parallel to a third line, then they are parallel to each other. 
3. If two lines which are not parallel do not intersect each other, they are known as skew lines, and these lines are not in the same plane.
4. There can be infinite lines, which are parallel to a plane but there is only one direction which is perpendicular to a plane
5. 2 points are always collinear; 3 points always lie in the same plane but 4 or more points may or may not lie in the same plane.
6. Three points which are not collinear, always lie on a circle.