Euclidean Geometry: A Brief Introduction
Euclidean Geometry is a branch of mathematics that deals with points, lines, and planes. In two-dimensional Euclidean geometry, also known as plane geometry, we deal with figures that lie on a flat surface. This surface is called a plane.
Points and Lines
In Euclidean geometry, a point is an undefined term which refers to something that has no dimensions and serves only as a location. On the other hand, a line is defined to be a straight path that extends in both directions without end. A line segment is then a part of the line between two points on the line. Lastly, we have rays which are like line segments except they have one endpoint and extend infinitely in one direction from that endpoint.
A plane can be thought of as a flat surface that contains all the points in a given straight line. In other words, it is a two-dimensional surface that has no thickness. Any two points on the same plane determine a straight line segment which lies entirely on that plane.
Euclidean geometry is the study of points, lines, and planes. It is considered to be the foundation of all other types of geometry. The main idea behind this branch of mathematics is the fact that any two points on the same plane determine a straight line segment which lies entirely on that plane. This allows us to study figures on a flat surface and develop formulas and proofs based on our findings.