Concepts Of Geometry

Elemental Concepts of Geometry
Geometry: is the branch of mathematics which studies the properties of geometric bodies in general. These properties refer to the measurements of bodies (length, area,volume etc.) as well as to the relations between their different parts.
The elemental geometric bodies are the point, the line and the plane. It is impossible to obtain an exact definition of theseconcepts because any attempt to define one of them it will always include the others, this makes it difficult to establish a hierarchical order to give sense to all definition. Therefore, we may find“definitions” such as:
* A point is the intersection of two non-parallel lines.
* A line is the intersection of two non-parallel planes.
* A plane is the set of all point determined bythree prefixed non-collinear planes.
Other elemental concepts of geometry
* If line r is fixed on the plane then the set consisting of all the points on the plane that are in the same side of theline, including r, is known as semi-plane.
* A surface is the set of all points that limit a geometric body. Every flat geometric body is a surface (also known as plane figure).
* Three pointsare collinear if they are Lying in the same line, and coplanar if they are lying in the same plane.
* Two lines are parallel if they are in the same plane and have no common point.
* Two planesare parallel if they have no point in common.
Axioms of the Euclidean Geometry
The following are some axioms of Euclidean Geometry:
* An undefined number of lines pass through one point.
*Two lines intersect as least in one point.
* Two points determine a line.
* Three non-collinear points determine a plane.
* A single line can be sketch parallel to the external point of agiven line.
Angles
If two semi-lines or rays have the same origin, then the union set of both is what we call an angle. Both semi-lines will be known as sides of the angle and the common...