Plane geometry, also known as Euclidean geometry, is the branch of geometry that involves the study of geometry in a plane. In this branch of geometry, we focus on studying the properties and relationships of figures that lie entirely within a two-dimensional plane. The plane is a flat surface that extends infinitely in all directions.

In plane geometry, we examine the properties of various geometric shapes such as points, lines, angles, triangles, quadrilaterals, circles, and polygons. These shapes are represented on a two-dimensional coordinate system, which consists of two perpendicular lines called the x-axis and the y-axis.

The study of plane geometry involves several key concepts and properties:

1. Points: Points are the basic building blocks of geometry. They have no size or shape and are represented by a dot.

2. Lines: Lines are made up of an infinite number of points and extend infinitely in both directions. They can be straight or curved.

3. Angles: Angles are formed when two lines intersect. They are measured in degrees and can be classified as acute, obtuse, right, or straight angles.

4. Triangles: Triangles are three-sided polygons. They have various classifications based on the lengths of their sides and the measures of their angles, such as equilateral, isosceles, scalene, acute, obtuse, or right triangles.

5. Quadrilaterals: Quadrilaterals are four-sided polygons. They include shapes such as squares, rectangles, parallelograms, trapezoids, and rhombuses.

6. Circles: Circles are perfectly round shapes. They consist of all points in a plane that are equidistant from a fixed center point.

7. Polygons: Polygons are closed figures with three or more sides. They can be regular or irregular and may have different numbers of sides.

Plane geometry is essential in various fields, including architecture, engineering, design, and art. It helps us understand and solve real-world problems involving shapes and figures in a two-dimensional space. By studying plane geometry, we can develop spatial reasoning skills, logical thinking, and problem-solving abilities.