Euclidean geometry is a branch of mathematics named after the ancient Greek mathematician Euclid. It is a system of geometry based on a set of axioms and logical deductions, which form the foundation for the study of shapes, sizes, and properties of geometric figures in a two-dimensional space.
 
Euclid’s most famous work is his book “Elements,” written around 300 BCE. In “Elements,” Euclid presents a comprehensive and systematic approach to geometry, consisting of definitions, postulates (axioms), and theorems. The book is divided into 13 books, each dealing with specific aspects of geometry, such as lines, angles, circles, triangles, and polyhedra.
 
Some key concepts and principles in Euclidean geometry include:
 
1. Points, Lines, and Planes: Euclidean geometry defines points as basic building blocks without size or dimension. Lines are straight paths extending infinitely in both directions, and planes are flat surfaces that extend infinitely in all directions.
 
2. Axioms and Postulates: Euclidean geometry is built upon a set of axioms or postulates, which are statements considered to be self-evident and accepted without proof. These axioms establish the fundamental properties and relationships of points, lines, and angles.
 
3. Euclidean Distance and Congruence: Euclidean geometry defines distance as the length between two points and uses it to determine congruence. Congruent figures have the same size and shape, meaning that corresponding sides and angles are equal.
 
4. Parallel Lines and Transversals: Euclidean geometry explores the properties of parallel lines and transversals. Parallel lines never intersect and maintain a constant distance from each other. Transversals are lines that intersect two or more other lines, forming various angle relationships.
 
5. Triangles and Polygons: Euclidean geometry studies the properties of triangles, including their angles, sides, and congruence criteria. It also extends to polygons, which are closed figures formed by connecting line segments.
 
6. Circle Geometry: Euclidean geometry includes the study of circles and their properties, such as central angles, inscribed angles, tangents, and chords.
 
Euclidean geometry forms the basis of many geometric principles and concepts that are still widely used today. While it primarily deals with two-dimensional space, its principles can be extended to three-dimensional geometry as well. Euclidean geometry has had a profound influence on mathematics, physics, architecture, engineering, and various other fields, providing a framework for understanding and analyzing geometric relationships.