The geometry as discipline math has several branches: Euclidean or flat, non – Euclidean, projective, space, among others. Spatial deals with the study of measurements and properties of different shapes that can be obtained from a combination of points, lines, angles and planes in space. In other words, the geometry of space studies three-dimensional geometric figures . Spatial Geometry
Spatial geometry complements Euclidean geometry that focuses on flat figures
On the other hand, this branch of mathematics is the theoretical basis for other areas such as trigonometry and analytic geometry.
Spatial geometry is based on two intuitive concepts, space and plane
Space refers to everything around us, therefore, it is the continent of everything that exists. This means that space is continuous, homogeneous , divisible and unlimited. Spatial Geometry
The concept of a plane can refer to any type of surface (a sheet, a table or a mirror). To represent a plane it is enough to draw a parallelogram.
A plan can be determined in four possible ways:
1) by three non-aligned points,
2) by a straight line and another outside point,
3) by two intersecting lines,
4) by two parallel lines.
From this it is possible to establish relative positions of lines and planes in space.
For example, two straight lines (lines) are parallel when they are in the same plane; two straight lines intersect when they have a common point, two straight lines are coincident when they have two points in common and overlap; two straight lines are transverse when they are not in the same plane and have no point in common.
Relative positions when presenting two planes in space
There are three types of possibilities: Spatial Geometry
1) two planes are parallel because they have no point in common,
2) two planes are intersecting when they have a line in common and they intersect,
3) two planes are coincident when they have three points in common that are not in a straight line, so one plane is superimposed on the other.
In addition to the positions of lines and planes, there are also the relative positions of a line and a plane, of which there are three options: parallel, intersecting and coincident. Spatial Geometry
All these principles based on points, lines and planes allow the construction of geometric space. In this sense, with these elements it is possible to calculate angles and establish their properties, algebraically express the elements of space or create geometric figures.