Geometry is a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids. It is one of the oldest branches of mathematics, going back at least to the times of Euclid, Pythagoras, and other natural philosophers of ancient Greece. Geometry is the visual study of shapes, sizes, and patterns, and how they fit together in space.

Some key concepts in geometry include:

• Points: A point is a location in space that has no size or shape. Almost everything in geometry starts with a point.

• Lines: A line is the shortest distance between two points. It has length but no width, which makes it one-dimensional. Wherever two or more lines meet, or intersect, there is a point, and the two lines are said to share a point.

• Planes: A plane is a flat surface that extends infinitely in all directions. It has length and width but no thickness, which makes it two-dimensional.

• Dimensions: In geometry, we work with objects that have different numbers of dimensions. For example, a point has zero dimensions, a line has one dimension, and a plane has two dimensions.

Geometry is used in many fields, including science, engineering, architecture, and art. It is also used in areas of mathematics that are apparently unrelated, such as number theory. Geometry is built on a mathematical ruleset, and we refer to these rules as axioms. There are five basic axioms in geometry that form the foundation for more complex problems.