Planar geometry, also known as Euclidean geometry, refers to the branch of mathematics that deals with the properties and relationships of figures and shapes in a flat, two-dimensional space called a plane. In planar geometry, all objects are considered to exist only in this plane, which has no depth or thickness.
The fundamental concept in planar geometry is a point, which represents a location in space and has no dimensions. Points can be connected to form straight lines, which are infinitely long and have no width. These lines can intersect, forming angles, and can be extended to form polygons, such as triangles, quadrilaterals, or polygons with any number of sides.
Planar geometry also involves the study of various properties of shapes, including their length, area, perimeter, and symmetries. It explores the different types of angles, such as acute, right, obtuse, and straight angles, as well as the classifications of polygons based on their sides and angles.
Additionally, planar geometry includes concepts like congruence, similarity, and transformations. Congruent shapes have the same shape and size, while similar shapes have the same shape but different sizes. Transformations, such as translations, rotations, and reflections, allow us to manipulate and move shapes around the plane without changing their properties.
Overall, planar geometry is essential in understanding and analyzing the properties and relationships of geometric shapes in a flat and two-dimensional setting. It provides the foundation for numerous mathematical principles and serves as a basis for more advanced branches of mathematics, such as analytic geometry and calculus.
